The ratio of Jenny’s savings to Linda’s

Question

The ratio of Jenny’s savings to Linda’s was 4 : 7 at first.  After Linda spent $80, the ratio of Jenny’s savings to Linda’s savings became 2 : 3.  How much money did each girl have at first?

Answer 1

X is the amount they have altogether

Jenny has (4/11)X and Linda has (7/11)X

LInda spent $80

Then Jenny has (2/5)(X-80) and LInda has(3/5)(X-80)

SO

(7/11)X - 80 = (3/5)(X-80)

35X - 4400 = 33(x-80)

35x - 4400 = 33x - 2640

2x = -2640 + 4400

2x = 1760

x=880

Altogether they have 880

At first Jenny has (4/11)(880) = 4*80 = 320

LInda has (7/11)(880) = 7*80 = 560

LInda spends 80...

That makes 800 left

Jenny has 320 out of 800 which is 32/80 = 2/5

LInda has 480 out of 800 which is 48/80 = 3/5

This shows the answer is correct