High School

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Cooper weighs 135 lbs and is gaining \( X \) lbs per week. Brittany weighs 143 lbs and is losing \( Y \) lbs per week. Write an equation that could be used to determine the number of weeks, \( x \), until Cooper and Brittany have the same weight.

Answer :

Final answer:

The equation to determine the number of weeks until Cooper and Brittany weigh the same is weeks = (143-135)/(X + Y), where X and Y are the pounds gained or lost each week respectively.

Explanation:

The subject of this problem is algebra and it involves creating an equation to solve for when two variable weights will be equal. The equation will involve the rate at which the weights are changing per week. We start with the initial weights given. Cooper weighs 135 lbs and is gaining X lbs per week. That can be written as weight = 135 + X*weeks. Brittany weighs 143 lbs and is losing Y lbs per week, which can be written as weight = 143 - Y*weeks. Here, 'weeks' is the common variable. The question asks for when will these two weights be equal, so we set the two equations equal to each other to solve for 'weeks'. That gives us 135 + X*weeks = 143 - Y*weeks. If we rearrange the equation, we will have (143-135) = (X + Y) * weeks. Thus weeks = (143-135)/(X + Y).

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