Operations - ACT Math
Card 0 of 20
Stella’s Soda Shop has a 24 oz bag of ice that they purchased for $22.50. In each drink they sell, they use 2 oz of ice. If the soda shop sold 4 drinks, what is the value of the ice left in the bag?
Stella’s Soda Shop has a 24 oz bag of ice that they purchased for $22.50. In each drink they sell, they use 2 oz of ice. If the soda shop sold 4 drinks, what is the value of the ice left in the bag?
If the cost of the bag is $22.50 and the bag holds 24 oz, each ounce is worth 94 cents. If Stella sold 4 drinks with 2 oz of ice each, she has used 8 oz of ice. 8 oz of ice at 94 cents an ounce is valued at $7.52. If you subtract that from the total value of the bag of ice, that leaves $14.98 worth of ice.
If you answered $18.74, you only valued the ice in each drink at one ounce.
If you answered $7.52, you found the value of ice in the drinks but not the value of the remainder of the bag.
If you answerd $3.76, you found the value of ice in the drinks if each drink only contained 1 ounce of ice.
If you answered $16.86, you just forgot to subtract the cost of ice for all four drinks but rather only subtracted the cost of ice for three drinks.
If the cost of the bag is $22.50 and the bag holds 24 oz, each ounce is worth 94 cents. If Stella sold 4 drinks with 2 oz of ice each, she has used 8 oz of ice. 8 oz of ice at 94 cents an ounce is valued at $7.52. If you subtract that from the total value of the bag of ice, that leaves $14.98 worth of ice.
If you answered $18.74, you only valued the ice in each drink at one ounce.
If you answered $7.52, you found the value of ice in the drinks but not the value of the remainder of the bag.
If you answerd $3.76, you found the value of ice in the drinks if each drink only contained 1 ounce of ice.
If you answered $16.86, you just forgot to subtract the cost of ice for all four drinks but rather only subtracted the cost of ice for three drinks.
Compare your answer with the correct one above
Solve the following equation.
Solve the following equation.
This question is testing the order of operations. For the equation 
, you must do the division problem first, then addition. 
.
This question is testing the order of operations. For the equation
Compare your answer with the correct one above
If 
, 
, and 
, what does 
equal?
If
To answer this question, we must substitute our given values into an equation and solve, remembering our order of operations.
First, we must take our values for each variable and substitute them into the equation given. Therefore, since we are told that , , and ,
Now that we have our values plugged in, we need to remember the order of operations in order to solve this problem. The order of operations goes as follows: parentheses, exponents, multiplication and division, and finally addition and subtraction. The first order of operations is to carry out any operations that are within parenthesis. Therefore, for this data:
We can now simply multiply these numbers together.
Our answer is 
.
To answer this question, we must substitute our given values into an equation and solve, remembering our order of operations.
First, we must take our values for each variable and substitute them into the equation given. Therefore, since we are told that
Now that we have our values plugged in, we need to remember the order of operations in order to solve this problem. The order of operations goes as follows: parentheses, exponents, multiplication and division, and finally addition and subtraction. The first order of operations is to carry out any operations that are within parenthesis. Therefore, for this data:
We can now simply multiply these numbers together.
Our answer is
Compare your answer with the correct one above
Steven is bowling in a tournament and has the highest average after five games, with scores of 
, 
, 
, 
, and 
. In order to maintain his average, what must be Steven's score on his sixth game?
Steven is bowling in a tournament and has the highest average after five games, with scores of
To answer this question, we must calculate the average of Steven's five games. After this, to maintain his average, he needs to score the same in his sixth game as his average.
To calculate the average of a set of numbers, you add all the values together (or get the sum) and divide by the total number of values. So, for this data:
We can then solve this fraction to get our average:
Steven's average over the first five games is a score of 
. In order to maintain his average, he must match his average in game six. So, our answer is a score of 
in game six.
To answer this question, we must calculate the average of Steven's five games. After this, to maintain his average, he needs to score the same in his sixth game as his average.
To calculate the average of a set of numbers, you add all the values together (or get the sum) and divide by the total number of values. So, for this data:
We can then solve this fraction to get our average:
Steven's average over the first five games is a score of
Compare your answer with the correct one above
A function 
is defined as 
. What is 
?
A function
To answer this question, we must substitute our value of 
into our equation for 
and follow our order of operations rules to solve for 
.
we first must substitute our known value into the equation. For this data:
We must now follow our order of operations to determine what we should do next. The order of operations goes as follows: parentheses, exponents, multiplication and division, and finally, addition and subtraction. So, for this equation, we must square the 
because solving for exponents comes before solving multiplication.
Note that when you square a number, you are multiplying it by itself. When we multiply two negative numbers, their product is positive.
We then multiply our two integers together and solve for 
:
Therefore, the answer to our question is 
.
To answer this question, we must substitute our value of
we first must substitute our known value into the equation. For this data:
We must now follow our order of operations to determine what we should do next. The order of operations goes as follows: parentheses, exponents, multiplication and division, and finally, addition and subtraction. So, for this equation, we must square the
Note that when you square a number, you are multiplying it by itself. When we multiply two negative numbers, their product is positive.
We then multiply our two integers together and solve for
Therefore, the answer to our question is
Compare your answer with the correct one above
To solve this question, we need to understand how absolute value works within an equation.
When numbers are within an absolute value sign (the numbers will be surrounded by 
), we need to use absolute value, or how far the number inside is away from zero. We must do any operations within the absolute value sign first. Therefore, the answer inside will always be positive, despite its sign, because you can't have negative distance from zero. So, for this data:
We can then just multiply our two integers in order to get our answer:
Therefore, our answer is 
.
To solve this question, we need to understand how absolute value works within an equation.
When numbers are within an absolute value sign (the numbers will be surrounded by
We can then just multiply our two integers in order to get our answer:
Therefore, our answer is
Compare your answer with the correct one above
A car averages 29 miles per gallon. If gas costs $3.75 per gallon how much money would need to be spent on gas to travel 1464.5 miles?
A car averages 29 miles per gallon. If gas costs $3.75 per gallon how much money would need to be spent on gas to travel 1464.5 miles?
The question is asking for the amount of money that would need to be spent on gas. Using the value given for the miles per gallon of the car and the amount of miles traveled it is possible to determine the gallons of fuel that will be required. This will be set up as 1464.5 miles travelled divided by the 29 miles per gallon that the car gets. This leaves us with 50.5 gallons of fuel used. From this point we can multiply the amount of fuel used, 50.5 gallons, by the price of fuel per gallon, $3.75, to obtain the amount of money that will spent on fuel, $189.38.
The question is asking for the amount of money that would need to be spent on gas. Using the value given for the miles per gallon of the car and the amount of miles traveled it is possible to determine the gallons of fuel that will be required. This will be set up as 1464.5 miles travelled divided by the 29 miles per gallon that the car gets. This leaves us with 50.5 gallons of fuel used. From this point we can multiply the amount of fuel used, 50.5 gallons, by the price of fuel per gallon, $3.75, to obtain the amount of money that will spent on fuel, $189.38.
Compare your answer with the correct one above
Connie's car gets 35 miles per gallon of gas. How much gas will she need to take a 525 mile trip? Round to the nearest gallon.
Connie's car gets 35 miles per gallon of gas. How much gas will she need to take a 525 mile trip? Round to the nearest gallon.
This becomes a division problem: 525 miles ÷ 35 miles per gallon = 15 gallons
This becomes a division problem: 525 miles ÷ 35 miles per gallon = 15 gallons
Compare your answer with the correct one above
A father buys a bag of marbles. He divides the marbles among his 5 children, who receive 24 marbles each. If there had been 6 children, how many marbles would each one get?
A father buys a bag of marbles. He divides the marbles among his 5 children, who receive 24 marbles each. If there had been 6 children, how many marbles would each one get?
There were a total of 120 marbles to begin with, since 5 * 24 = 120.
If the marbles are split between 6 children, then each child gets 120/6 = 20 marbles each.
There were a total of 120 marbles to begin with, since 5 * 24 = 120.
If the marbles are split between 6 children, then each child gets 120/6 = 20 marbles each.
Compare your answer with the correct one above
At the end of December, Abraham adds the average number of stamps he has been collecting over the year to his album, how many stamps will he have at the end of December?
At the end of December, Abraham adds the average number of stamps he has been collecting over the year to his album, how many stamps will he have at the end of December?
In 11 months, Abraham has collected 155 stamps, or an average of 
stamps per month. At the end of December, he should have 
stamps.
In 11 months, Abraham has collected 155 stamps, or an average of
Compare your answer with the correct one above
Sam is paid $15 per hour for laying bricks. If he lays 3,000 bricks at a rate of 5 bricks per minute, how much will he be paid?
Sam is paid $15 per hour for laying bricks. If he lays 3,000 bricks at a rate of 5 bricks per minute, how much will he be paid?
First we need to convert some units. If Sam lays 5 bricks per minute, then multiply that figure by 60 to find that he lays 300 bricks per hour. 3,000 bricks divided by 300 bricks/hour means he worked for 10 hours. Therefore, when we mutiply $15/hour by 10 hours, we see he makes $150.
First we need to convert some units. If Sam lays 5 bricks per minute, then multiply that figure by 60 to find that he lays 300 bricks per hour. 3,000 bricks divided by 300 bricks/hour means he worked for 10 hours. Therefore, when we mutiply $15/hour by 10 hours, we see he makes $150.
Compare your answer with the correct one above
Each variable f, g, h, i, and j represents a positive real number. Considering the equations below, which of the four variables g, h, i, or j necesarily has the greatest value?
1.75g = f
1.69h = f
1.23i = f
0.46j = f
Each variable f, g, h, i, and j represents a positive real number. Considering the equations below, which of the four variables g, h, i, or j necesarily has the greatest value?
1.75g = f
1.69h = f
1.23i = f
0.46j = f
All four variables are positive real numbers. Each variable g, h, i, and j are multiplied by differing values to obtain the same value f. Since j is multiplied by the smallest value to obtain f it must be the greatest value. In this manner we could determine that g is necesarily the smallest value.
All four variables are positive real numbers. Each variable g, h, i, and j are multiplied by differing values to obtain the same value f. Since j is multiplied by the smallest value to obtain f it must be the greatest value. In this manner we could determine that g is necesarily the smallest value.
Compare your answer with the correct one above
Joey is beginning to invest in the stock market. He purchased 150 shares of a cell phone company. The company pays a dividend of $2.55 per share. What is his total dividend?
Joey is beginning to invest in the stock market. He purchased 150 shares of a cell phone company. The company pays a dividend of $2.55 per share. What is his total dividend?
The words "per share" clues us into a multiplication problem, 150 * 2.55 = 382.50
The words "per share" clues us into a multiplication problem, 150 * 2.55 = 382.50
Compare your answer with the correct one above
George is buying his first car. He has $500 for a downpayment and can afford monthly payments of $175 for three years. What is the most expensive car he can purchase?
George is buying his first car. He has $500 for a downpayment and can afford monthly payments of $175 for three years. What is the most expensive car he can purchase?
The most expensive car he can purchase is given by the total of all monthly payments and the down payment: $175 per month * 12 months per year * 3 years + $500 down = $6,800
The most expensive car he can purchase is given by the total of all monthly payments and the down payment: $175 per month * 12 months per year * 3 years + $500 down = $6,800
Compare your answer with the correct one above
A hockey team wants to purchase uniforms for its 26 players, 2 of which are goalies. It costs $40 for a one-time designing fee. It costs $24 for goalie jerseys and $20 for all other jerseys. How much does it cost to purchase all of the uniforms?
A hockey team wants to purchase uniforms for its 26 players, 2 of which are goalies. It costs $40 for a one-time designing fee. It costs $24 for goalie jerseys and $20 for all other jerseys. How much does it cost to purchase all of the uniforms?
There are 24 normal players and 2 goalies. Thus we can represent the sum in the equation 24($20) + 2($24) + $40 = $568.
There are 24 normal players and 2 goalies. Thus we can represent the sum in the equation 24($20) + 2($24) + $40 = $568.
Compare your answer with the correct one above
Which of the following expressions must be an even integer if x is an integer?
Which of the following expressions must be an even integer if x is an integer?
An integer raised to an even power always yields an even integer. All of the other expressions could yield odd integers.
An integer raised to an even power always yields an even integer. All of the other expressions could yield odd integers.
Compare your answer with the correct one above
Jordan is packing his lunch, and has decided to bring one piece of fruit, one vegetable, one type of sandwich, and one drink. How many different combinations of lunch can Jordan pack?
Fruit Vegetable Sandwich Drink Apple Carrot Turkey Milk Banana Celery Chicken Water Orange Veggie
Jordan is packing his lunch, and has decided to bring one piece of fruit, one vegetable, one type of sandwich, and one drink. How many different combinations of lunch can Jordan pack?
| Fruit | Vegetable | Sandwich | Drink |
|---|---|---|---|
| Apple | Carrot | Turkey | Milk |
| Banana | Celery | Chicken | Water |
| Orange | Veggie |
To find the number of different combinations, we must use the fundamental counting principal to multiply the number of options in each category together:
(3)(2)(3)(2) = 36
To find the number of different combinations, we must use the fundamental counting principal to multiply the number of options in each category together:
(3)(2)(3)(2) = 36
Compare your answer with the correct one above
If 
, approximately how many cm are in 
If
Use the factor-label method for conversion:
The units are considered like numbers and can be cancelled out of both the numerator and the denominator.
Use the factor-label method for conversion:
The units are considered like numbers and can be cancelled out of both the numerator and the denominator.
Compare your answer with the correct one above
Given 
, convert 60 miles per hour to approximate feet per second.
Given
Using the factor-label method we get:
approximately equals 
The units are treated like numbers and are cancelled when they are in both the numerator and denominator.
Using the factor-label method we get:
approximately equals
The units are treated like numbers and are cancelled when they are in both the numerator and denominator.
Compare your answer with the correct one above
On an airline flight of 250 people there is a choice of pasta, salad, or pizza for dinner. If 113 passengers choose pasta and 30% choose salad, how many passengers choose pizza?
On an airline flight of 250 people there is a choice of pasta, salad, or pizza for dinner. If 113 passengers choose pasta and 30% choose salad, how many passengers choose pizza?
30% of 250 is 75. Therefore, 250 – 75 – 113 = 62
30% of 250 is 75. Therefore, 250 – 75 – 113 = 62
Compare your answer with the correct one above