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
<pre>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 {{{matrix(1,5, 2/3, of, "b,", or, 2b/3)}}}
After paying his portion of bill, Jack had {{{5x  -  2b/3}}} left, which was $126
So, we get: {{{matrix(1,3, 5x  -  2b/3, "=", 126 )}}}
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 {{{matrix(1,5, 1/3, of, "b,", or, b/3)}}}
After paying her portion of bill, Jill had .8(2x) left
So, we get: {{{matrix(1,7, 2x  -  b/3, "=", .8(2x), "=====>", 2x  -  b/3, "=", 1.6x)}}} 
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)
{{{matrix(1,5, x, "=", 378/12.6, "=", 30)}}}
 
1.2(30)  -  b = 0 --- Substituting 30 for x in eq (ii)
36  -  b = 0
36 = 0 + b
b, or {{{highlight_green(matrix(1,3, bill, "was:", "$36"))}}}