Question

A furniture maker has 92 in. of decorative cord that she must cut into two pieces to put on a sofa. One piece must be 24 in. shorter than the other. Find the length of each piece."

Answer 1

The furniture maker will have two pieces of decorative cord, one 58 inches long and the other 34 inches long, to cover the required total of 92 inches.

Step-by-step explanation:

The furniture maker has 92 inches of decorative cord to cut into two pieces. One piece needs to be 24 inches shorter than the other. To find the lengths of the two pieces, we set up an equation where one piece is represented by x and the other piece by x - 24. Since the total length of the cord is 92 inches, we can write the equation as x + (x - 24) = 92. Solving for x, we get:

2x - 24 = 922x = 116x = 58

So, one piece is 58 inches long. The other piece would then be 58 - 24, which equals 34 inches. Hence, the two pieces of decorative cord are 58 inches and 34 inches long respectively.