SOLUTION: At the Cafe, a lunch of iced tea, a veggie burger, and fries costs $7.56, with the fries costing twice as much as the iced tea. Next week at the Cafe, the price of the iced tea wil

Question 1038941: At the Cafe, a lunch of iced tea, a veggie burger, and fries costs $7.56, with the fries costing twice as much as the iced tea. Next week at the Cafe, the price of the iced tea will increase 10% and the price of the veggie burger will increase 25%. After the increase, the same lunch purchase will cost $8.68. Find the price of each item before the increase (round to the nearest penny).
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the cost of iced tea the 1st week
Let = the cost of a veggie burger the 1st week
Let = the cost of the fries the 1st week
----------------------------------------------
(1) ( in cents )
(2) ( in cents )
(3) ( in cents )
--------------------------------------
Multiply both sides of (3) by
(3)
Multiply both sides of (1) by
and subtract () from (2)
(3)
(1)
------------------------------------
(4)
Substitute (2) into (1)
(1)
(1)
Multiply both sides of (1) by and
subtract (4) from (1)
(1)
(4)
----------------------------

and
(2)
(2)
and
(1)
(1)
(1)
(1)
-----------------------------
Convert to dollars since answers are in cents:

The cost of iced tea the 1st week was $1.18
The cost of a veggie burger the 1st week was $4.01
The cost of the fries the 1st week was $2.37
------------------
check the answers:
(1) ( in dollars )
(1)
(1)
and
(2)
(2)
(2)
close enough
and
(3) ( in dollars )
(3)
(3)
(3)
OK when rounded off
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