How to add integers - SAT Math
Card 0 of 5
Find the values of the variables 
and 
in the following sequence:
Find the values of the variables
Terms are obtained by alternately adding 5 and multiplying by 3:
The missing two elements are found by multiplying by 3, then by adding 5:
Multiplying by 3 confirms that this is correct:
Terms are obtained by alternately adding 5 and multiplying by 3:
The missing two elements are found by multiplying by 3, then by adding 5:
Multiplying by 3 confirms that this is correct:
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My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?
My sister invited me to play an online word game. In the game vowels (a,e,i,o,u) are worth 3 points and consonants are worth 5. How much would I score if I use the word “University” ?
In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.
In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.
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What is the sum of multiples of 10 from 10 to 140 inclusive?
What is the sum of multiples of 10 from 10 to 140 inclusive?
Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.
Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.
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Examine the sequence:
Give the number that replaces the square.
Examine the sequence:
Give the number that replaces the square.
After the first term, the next four terms are obtained by adding, multiplying, subtracting, and dividing by 2, in order. The four terms after that are obtained by carrying out the same operations with 4. The next term is obtained by adding 6, so the operations can be expected to be repeated with 6, the next even number.
Observe the operations as carried out with 2:
Carrying out the same steps, in order, with 4:
Carrying out the same steps, in order, with 6:
, the number that replaces the circle;
, the number that replaces the square.
After the first term, the next four terms are obtained by adding, multiplying, subtracting, and dividing by 2, in order. The four terms after that are obtained by carrying out the same operations with 4. The next term is obtained by adding 6, so the operations can be expected to be repeated with 6, the next even number.
Observe the operations as carried out with 2:
Carrying out the same steps, in order, with 4:
Carrying out the same steps, in order, with 6:
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The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?
The sum of three consecutive even numbers is 42. What is the smallest even number in this sequence?
To solve this problem. First set up a mathematical equation that represents this scenario.
"The sum of three consecutive even numbers is 42."
Let
and recalling that each consecutive even number is two values greater that the previous even number, the mathematical equation becomes
From here isolate the variable on one side of the equations with all other constants on the other side.
Subtract six from both sides.
Now divide by three.
Since 
represents the beginning number in this sequence it also represents the smallest even number in this sequence. Therefore the smallest even number is 12.
To solve this problem. First set up a mathematical equation that represents this scenario.
"The sum of three consecutive even numbers is 42."
Let
and recalling that each consecutive even number is two values greater that the previous even number, the mathematical equation becomes
From here isolate the variable on one side of the equations with all other constants on the other side.
Subtract six from both sides.
Now divide by three.
Since
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