A rectangular piece of cardboard is 3 ft 11 in long and 2 ft 4 in wide. What the maximum number of 5 in by 8 in rectangles that can be cut from it?

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UpStudy AI · Accepted Answer

To solve the problem, we need to follow these steps:

1. **Convert the dimensions of the cardboard from feet and inches to inches only.**
2. **Calculate the area of the cardboard.**
3. **Calculate the area of one of the smaller rectangles (5 in by 8 in).**
4. **Determine how many of the smaller rectangles can fit into the area of the cardboard.**

### Step 1: Convert dimensions to inches

- The length of the cardboard is 3 ft 11 in.
  - Convert feet to inches: $$3 \text{ ft} = 3 \times 12 = 36 \text{ in}$$
  - Total length in inches: $$36 \text{ in} + 11 \text{ in} = 47 \text{ in}$$

- The width of the cardboard is 2 ft 4 in.
  - Convert feet to inches: $$2 \text{ ft} = 2 \times 12 = 24 \text{ in}$$
  - Total width in inches: $$24 \text{ in} + 4 \text{ in} = 28 \text{ in}$$

### Step 2: Calculate the area of the cardboard

The area $$A_c$$ of the cardboard can be calculated using the formula:
$$
A_c = \text{length} \times \text{width} = 47 \text{ in} \times 28 \text{ in}
$$

### Step 3: Calculate the area of one of the smaller rectangles

The area $$A_r$$ of one of the smaller rectangles (5 in by 8 in) is:
$$
A_r = 5 \text{ in} \times 8 \text{ in}
$$

### Step 4: Determine how many rectangles can fit

To find the maximum number of rectangles that can be cut from the cardboard, we divide the area of the cardboard by the area of one rectangle:
$$
\text{Number of rectangles} = \frac{A_c}{A_r}
$$

Now, let's perform the calculations.

1. Calculate $$A_c$$.
2. Calculate $$A_r$$.
3. Calculate the number of rectangles.

Let's do these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$47\times 28$$
- step1: Multiply the numbers:
  $$1316$$
Calculate or simplify the expression $$ 5 * 8 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5\times 8$$
- step1: Multiply the numbers:
  $$40$$
Calculate or simplify the expression $$ 1316 / 40 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1316}{40}$$
- step1: Reduce the fraction:
  $$\frac{329}{10}$$
Now that we have the necessary calculations:

1. The area of the cardboard $$A_c$$ is $$1316 \text{ in}^2$$.
2. The area of one of the smaller rectangles $$A_r$$ is $$40 \text{ in}^2$$.

### Step 4: Calculate the number of rectangles

To find the maximum number of rectangles that can be cut from the cardboard, we divide the area of the cardboard by the area of one rectangle:
$$
\text{Number of rectangles} = \frac{1316}{40} = 32.9
$$

Since we cannot cut a fraction of a rectangle, we take the whole number part. Therefore, the maximum number of 5 in by 8 in rectangles that can be cut from the cardboard is:

$$
\boxed{32}
$$
The maximum number of 5 in by 8 in rectangles that can be cut from the cardboard is 32.

A rectangular piece of cardboard is 3 ft 11 in long and 2 ft 4 in wide. What the maximum number of 5 in by 8 in rectangles that can be cut from it?

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