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Three desks and a bookcase together weigh 157 pounds. The bookcase weighs 34 pounds. Which equation could help determine how much each desk weighs?

Let \( x \) represent the weight of each desk.

A. \( 3x + 34 = 157 \)

Answer :

Final answer:

To find out how much each desk weighs, you can use the equation:[tex]\(3\text{ desks} + \text{bookcase} = 157\text{ pounds} - \text{bookcase weight}\).[/tex]

Explanation:

To determine the weight of each desk, we can set up an equation based on the given information. Let [tex]\(D\)[/tex] represent the weight of each desk in pounds, and [tex]\(B\)[/tex] represent the weight of the bookcase, which is 34 pounds.

We know that three desks weigh three times the weight of one desk, so the total weight of the desks is [tex]\(3D\)[/tex] pounds. Adding the weight of the bookcase to this total should equal the total weight of three desks and the bookcase together, which is 157 pounds:

[tex]\(3D + B = 157\)[/tex]

Substituting the weight of the bookcase, which is 34 pounds, into the equation:

[tex]\(3D + 34 = 157\)[/tex]

Now, we can solve for [tex]\(D\)[/tex] by isolating it on one side of the equation:

[tex]\(3D = 157 - 34\)[/tex]

[tex]\(3D = 123\)[/tex]

Finally, divide both sides by 3 to find the weight of each desk:

[tex]\(D = \frac{123}{3} = 41\) pounds[/tex]

So, each desk weighs 41 pounds.

In summary, the equation [tex]\(3D + B = 157\)[/tex] helps us find the weight of each desk, and after solving for [tex]\(D\)[/tex], we find that each desk weighs 41 pounds.

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