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Algebra / Linear equations in two variables Difficulty: Medium

$24.5 x + 24.75 y = 641$

Isabel ordered topsoil and crushed stone, which cost a total of $dollar sign 641$ , for her garden. The given equation represents the relationship between the number of cubic yards of topsoil, $x$ , and the number of tons of crushed stone, $y$ , Isabel ordered. How much more, in dollars, did a ton of crushed stone cost Isabel than a cubic yard of topsoil?

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Explanation

The correct answer is $.25$ . It’s given that the topsoil and crushed stone Isabel ordered for her garden cost a total of $dollar sign 641$ . It’s also given that the equation $24.5 x + 24.75 y = 641$ represents the relationship between the number of cubic yards of topsoil, $x$ , and the number of tons of crushed stone, $y$ , that Isabel ordered. Since $x$ represents the number of cubic yards of topsoil ordered, $24.5 x$ represents the total cost, in dollars, of the topsoil, and the cost per cubic yard of topsoil is $dollar sign 24.50$ . Similarly, since $y$ represents the number of tons of crushed stone ordered, $24.75 y$ represents the total cost, in dollars, of crushed stone ordered, and the cost per ton of crushed stone is $dollar sign 24.75$ . Therefore, a ton of crushed stone cost Isabel $24.75 minus 24.50$ , or $0.25$ , more dollars than a cubic yard of topsoil. Note that .25 and 1/4 are examples of ways to enter a correct answer.