Question

Ruby bought 8 notebooks for $24.50. Some of the notebooks were $2.50 each, and others were $3.25 each. If x represents the number of least expensive notebooks, which equation can be used to find the number of least expensive notebooks purchased?

Answer 1

equation: 24.50 = 2.50x + 3.25(8 -x)

solution: x = 2

Explanation:

You can solve this problem by writing an equation for the total value of the purchase. It is the sum of products of the number of notebooks and their cost.

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If x of the 8 notebooks were the least expensive, then (8-x) were the most expensive.

total cost = cost of least expensive + cost of most expensive

24.50 = 2.50x + 3.25(8 -x) . . . . . . . . one way to write the equation

24.50 = -0.75x +26.00 . . . . . . . . . simplified equation

-1.50 = -0.75x . . . . . . . . . . . . . . . after subtracting 26

2 = x . . . . . . . . . . . . divide by -0.75

Two (2) of the least-expensive notebooks were purchased.

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Additional comments

This problem statement asks "which equation," but does not provide any choices. We hope that one of the equations shown above will give you a sufficient clue to make the correct answer choice.

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We like to let the variable represent the most-expensive contributor in the problem. That way, it ends up with a positive coefficient when the equation is simplified. There tends to be fewer errors when the math is done with positive numbers.