Sara and Jenny can both do flips in the air. The ratio of the number of flips Sara can do to the number of flips Jenny can do is 3:8. Jenny can do 120 more flips than Sara. If Sara increases the number of her flips by 3 and Jenny decreases the number of her flips by 12, what will be the new ratio of the number of flips Sara can do to the number of flips Jenny can do?

Wow! I never had problems this hard in middle school!

But you can do it!

First, we need to figure the number of flips Sara can do based on Jenny's.

Jenny = 120 and Sara - 120 x 3/8 (because she is only 3/8 of Sara's)

Calculate 120 x 3/8 = 45 flips

Now we know that Sara increased her amount of flips by 3 (45 + 3 = 48)

And we know that Jenny decreased hers by 12 (120 - 12 = 108)

So now we have a ratio of 48:108, but we need to simplify that with factoring.

I am going to divide first by 2.

24:54

Then 2 again ...

12:27

How about 3?

4:9

I think that is as far as we can go.

Sara is now doing 4 out of every 9 that Jenny does.

Check it!

108 (Jenny) x 4/9 = 48 (Sara) Yes! It checks.