Sara and David had $420 altogether. Sara spent 2/5 of her money and David spent $120. After spending, Sara had twice as much money as David. How much money did David have at first?

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mr.tan

I think something is wrong with the numbers. My solution is below but the money is in fractions of 13.

THOUGHT PROCESSWhen we see 2/5, we might have the impulse to draw 5 units with 2 spent and 3 remaining. However the 3 remaining is twice as much as David's, which means we have to cut the units in halves. So it is better to do 10 units instead of 5.MODEL

WORKING10 u + 3u + 120 = 420 u = 300/13 At first, David had 3u + 120 = 900/13 + 120 = $189 3/13.CHECK:Sara David Before: 230 10/13 189 3/13 (TOTAL: 420) After: 1800/13 900/13 (Sara = 2 x David)

MsHuppy

Thanks! I was getting decimals too!