Question 1032212

Bethany’s credit card bill in December was 1.5 times her food bill. Her apartment rent was 5 times her utility bill. Her phone bill was $17 less than half of her food bill. Her phone bill was also $18 less than twice her utilities bill. The total of the five bills was $751. What was the amount of each bill?
<pre>Let the amount for food, and utilities be F, and U, respectively
Then amount for credit card = 1.5F
Amount for rent = 5U
Amount for phone = {{{matrix(1,3, (1/2) * F - 17, or, F/2 - 17)}}}
Also, amount for phone = 2U - 18
We can then say that: {{{F/2 - 17 = 2U - 18}}}
F - 34 = 4U - 36 -------- Multiplying by LCD, 2
F = 4U - 36 + 34
F = 4U - 2
Since all sum to $751, we then get: U + 1.5(4U - 2) + 5U + 2U - 18 + 4U - 2 = 751
U + 6U - 3 + 5U + 2U - 18 + 4U - 2 = 751
18U - 23 = 751
18U = 751 + 23
18U = 774
U, or amount for utilities = {{{774/18}}}, or {{{highlight_green("$"43)}}}
Amount for food: 4(43) - 2 = 172 - 2, or {{{highlight_green("$"170)}}}
Amount for credit card: 1.5(170) = {{{highlight_green("$"255)}}}
Amount for phone: 2(43) - 18 = 86 - 18 = {{{highlight_green("$"68)}}}
Amount for rent: 5(43) = {{{highlight_green("$"215)}}}