Question

Sara and jenny can both do flips in the air. the ratio to the number of flips that sara can do to jenny is 3:8. jenny can do 120 more flips than sara. if sara increases the number of flips she does by 3 and jenny decreases hers by 12, what will the new ratio be?

Answer 1

Given ratio :

Sara flips : Jenny flips = 3:8.

Let us assume Sara flips = x

We are given "Jenny can do 120 more flips than sara".

Therefore, 120 more than x could be given by expression " x+120".

In terms of x Jenny can flips = x+120.

The ratio of Sara flips to Jenny = 3:8.

Setting up proportion now,

x : x+120 : : 3:8

Writing in fraction form

`(x)/(x+20)=(3)/(8)`

On cross multiplication, we get

`x*8 = 3*(x+120)`

8x = 3(x+120).

Distributing 3 on right side.

8x = 3*x +3*120

8x = 3x + 360

Subtracting 3x from both sides

8x-3x = 3x-3x+360

5x = 360

Dividing both sides by 5, we get

5x/5 = 360/5

x=72.

120 more than 72 = 72+120 = 192.

Therefore, Sara flips = 72 and Jenny flips = 192 in originaly.

Increasing Sara's number of flips by 3 and decreasing Jenny's number of flips by 12, we get

Sara flips = 72+3 = 75 and Jenny flips = 192-12 = 180.

New ratio would be
`(75)/(180)` =
`(5)/(12)`.

So, the new ratio would be 5:12.