Question

Use the clues to write equations. Use the equations to solve the problem.

Feng is a carpenter. Use the clues to find out how many maple and walnut boards Feng buys.
Clue 1: Feng buys maple boards for $7 each, and walnut boards for $9 each. He spends $46 altogether.
Clue 2: The number of maple boards equals twice the number of walnut boards.
Clue 3: The number of maple boards is even.
(a) m = 2w, 7m + 9w = 46
(b) m = 2w, 7m - 9w = 46
(c) m = 3w, 7m + 9w = 46
(d) m = 2w, 7m + 9w = 56

Answer 1

By creating and solving a system of equations from the provided clues, it is determined that Feng buys 4 maple boards and 2 walnut boards.

Step-by-step explanation:

First, let's use the given clues to write the equations. Clue 1 and Clue 2 together imply that the number of maple boards (m) is twice the number of walnut boards (w), so we have m = 2w. Clue 1 also states that Feng spends $46 altogether, buying maple boards for $7 each and walnut boards for $9 each, so our second equation is 7m + 9w = 46.

Solving this system of equations:

• Replace m with 2w in the second equation: 7(2w) + 9w = 46.
• Simplify and solve for w: 14w + 9w = 46, which gives us 23w = 46.
• Divide both sides by 23 to find w: w = 2.
• Now solve for m: m = 2w = 2(2) = 4.

Therefore, Feng buys 4 maple boards and 2 walnut boards.