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Solving a value mixture problem using a system of linear...
Michael
The Foster family and the Young family each used their sprinklers last summer. The water output rate for the Foster family's sprinkler was $15 L$ per hour. The water output rate for the Young family's sprinkler was $35 L$ per hour. The families used their sprinklers for a combined total of 40 hours, resulting in a total water output of 900 L. How long was each sprinkler used?
Foster family's sprinkler: Ø1 hours
Young family's sprinkler: $◻$ hours
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Final Answer: The Foster family's sprinkler was used for $25$ hours and the Young family's sprinkler was used for $15$ hours.

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Step 1 ：Translate the problem into a system of linear equations. Let's denote the time the Foster family's sprinkler was used as x and the time the Young family's sprinkler was used as y. Then we have two equations: $x + y = 40$ (total time) and $15 x + 35 y = 900$ (total water output).

Step 2 ：Solve the system of equations to find the values of x and y. The solution is $x = 25$ , $y = 15$ .

Step 3 ：Final Answer: The Foster family's sprinkler was used for $25$ hours and the Young family's sprinkler was used for $15$ hours.

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