SOLUTION: The operators of a national park want to be more water efficient. They decide to start with the park's comfort stations. First, they purchase one washing machine and four shower he
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Question 1105152: The operators of a national park want to be more water efficient. They decide to start with the park's comfort stations. First, they purchase one washing machine and four shower heads front for S900. Then, they purchase ten washers and eight shower heads for $8200. What is the cost of each washing machine? What is the cost of each shower head? Answer by greenestamps(13200) (Show Source):
If the first purchase had been twice as big, they would have purchased 2 washers and 8 shower heads, for $1800.
The second purchase was 10 washers and 8 shower heads, for $8200.
The number of shower heads is now the same in both purchases, so the difference of $6400 in the cost is because of 8 more washers.
So the cost of each washer is $6400/8 = $800.
Then since the first purchase was 1 washer and 4 shower heads for $900, the 4 shower heads cost $100, so each shower head costs $25.
And now a standard algebraic solution....
let x = cost of each washer
let y = cost of each shower head
(1) 1 washer and 4 shower heads cost $900
(2) 10 washers and 8 shower heads cost $8200
Multiply the first equation by 2:
(3)
Subtract (3) from (2), eliminating y:
(4)
Substitute (4) in (1) to solve for y:
(5)
Surprise! The algebraic solution was just a formal way of doing EXACTLY what the informal solution did....
