Question

Eleanor and Max used two rectangular pieces of plywood, placed end-to-end, to make a long rectangular stage for the school play. One board was 4 feet long, and the other was 4 1/2 feet long. The two pieces of plywood had equal widths. The total area of the stage was 57 3/8 square feet. What was the width of the plywood?

a. 2 1/8 feet
b. 2 3/8 feet
c. 2 5/8 feet
d. 2 7/8 feet

Answer 1

The total length of the stage is 8 1/2 feet. By setting up an equation using the formula for the area of a rectangle, we can solve for the width of the plywood, which is 2 1/8 feet.

Step-by-step explanation:

To find the width of the plywood, we need to find the length of the stage. The problem states that the two rectangular pieces of plywood were placed end-to-end to make a long rectangular stage. One board was 4 feet long, and the other was 4 1/2 feet long. So the total length of the stage is 4 + 4 1/2 = 8 1/2 feet.

We can use the formula for finding the area of a rectangle (length x width) to set up an equation. Let's say the width of the plywood is w feet. The total area of the stage is 57 3/8 square feet. So, we have the equation: (8 1/2)(w) = 57 3/8. We can solve this equation to find the width of the plywood.

First, let's convert 8 1/2 to an improper fraction: 8 1/2 = 17/2.

Multiplying both sides of the equation by 2, we get: 17w = 57 3/8 x 2 = 57 3/8 x 16/8 = 916/8.

Now, divide both sides of the equation by 17 to solve for w: w = (916/8) / 17 = 916/136 = 2/8 = 1/4.

So, the width of the plywood is 1/4 feet, which can be simplified to 2 1/8 feet.