SOLUTION: 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

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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): You can put this solution on YOUR website!
Let = amount of Jack's money
Let = amount of Jill's money
--------------------------------------------



------------------------------------
by substitution:





-----------------------


and


-------------------------------

The bill was $15.75
-------------------------------
check:



OK
check the math & get a 2nd opinion if needed



Answer by MathTherapy(10555)   (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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