How to find inverse variation - SAT Math
Card 0 of 5
A school's tornado shelter has enough food to last 20 children for 6 days. If 24 children ended up taking shelter together, for how many fewer days will the food last?
A school's tornado shelter has enough food to last 20 children for 6 days. If 24 children ended up taking shelter together, for how many fewer days will the food last?
Because the number of days goes down as the number of children goes up, this problem type is inverse variation. We can solve this problem by the following steps:
20*6=24*x
120=24x
x=120/24
x=5
In this equation, x represents the total number of days that can be weathered by 24 students. This is down from the 6 days that 20 students could take shelter together. So the difference is 1 day less.
Because the number of days goes down as the number of children goes up, this problem type is inverse variation. We can solve this problem by the following steps:
20*6=24*x
120=24x
x=120/24
x=5
In this equation, x represents the total number of days that can be weathered by 24 students. This is down from the 6 days that 20 students could take shelter together. So the difference is 1 day less.
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Find the inverse equation of:
Find the inverse equation of:
To solve for an inverse, we switch x and y and solve for y. Doing so yields:
To solve for an inverse, we switch x and y and solve for y. Doing so yields:
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x y 
If 
varies inversely with 
, what is the value of 
?
| x | y |
|---|---|
| |
| |
| |
| |
If
An inverse variation is a function in the form: 
or 
, where 
is not equal to 0.
Substitute each 
in 
.
Therefore, the constant of variation, 
, must equal 24. If 
varies inversely as 
, 
must equal 24. Solve for 
.
An inverse variation is a function in the form:
Substitute each
Therefore, the constant of variation,
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Find the inverse equation of 
.
Find the inverse equation of
1. Switch the 
and 
variables in the above equation.
2. Solve for 
:
1. Switch the
2. Solve for
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When 
, 
.
When 
, 
.
If 
varies inversely with 
, what is the value of 
when 
?
When
If
If 
varies inversely with 
, 
.
1. Using any of the two 
combinations given, solve for 
:
Using 
:
2. Use your new equation 
and solve when 
:
If
1. Using any of the two
Using
2. Use your new equation
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