Question 1147256: Hi
jack and jill had some money in the ratio of 5:2. They jointly paid for a restaurant bill respectively in the ratio of 2:1. If jill spent 20 percent of her money and jack had 126 dollars left, how much was the bill.
thanks
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441)   (Show Source):
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website! Hi
jack and jill had some money in the ratio of 5:2. They jointly paid for a restaurant bill respectively in the ratio of 2:1. If jill spent 20 percent of her money and jack had 126 dollars left, how much was the bill.
thanks
With Jack to Jill's ratio being 5:2, and with the multiplicative factor being x, we can say that the original amounts Jack and Jill had were: 5x and 2x
With a 2:1 bill-ratio, and b being the amount of the bill, Jack paid 
After paying his portion of bill, Jack had  left, which was $126
So, we get: 
15x - 2b = 378 ------ Multiplying by LCD, 3 ------- eq (i)
With a 2:1 bill-ratio, and b being the amount of the bill, Jill paid 
After paying her portion of bill, Jill had .8(2x) left
So, we get: 
6x - b = 4.8x ------ Multiplying by LCD, 3
6x - 4.8x - b = 0
1.2x - b = 0 --------- eq (ii)
- 2.4x + 2b = 0 ------ Multiplying eq (ii) by - 2 ------- eq (iii)
12.6x = 378 ---------- Adding eqs (iii) & (i)
1.2(30) - b = 0 --- Substituting 30 for x in eq (ii)
36 - b = 0
36 = 0 + b
b, or 
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