A graphic designer created an image for a school banner. He uses this image for small and medium banners. To produce a large banner, the designed increase the size of the image by 12.5% to 18 inches tall by 22.5 inches wide. What was the size of the original image?

Options

A. 15 inches by 17.5 inches
B. 15 inches by 18 inches
C. 16 inches by 18.5 inches
D. 16 inches by 20 inches

Explanation

To find the size of the original image before the designer increased its dimensions by 12.5%, we can follow these steps:

### Step 1: Understand the increase in dimensions
The designer increased the dimensions of the image by 12.5%. This means the new dimensions (after the increase) represent 112.5% of the original dimensions.

### Step 2: Set up the equations
Let the original height of the image be \( H \) inches and the original width be \( W \) inches. After the increase, the height and width are given as:
- Height = 18 inches
- Width = 22.5 inches

We can express this mathematically as:
- \( 112.5\% \) of \( H = 18 \)
- \( 112.5\% \) of \( W = 22.5 \)

### Step 3: Convert percentages to decimal
To convert 112.5% to a decimal, we divide by 100:
\[ 112.5\% = \frac{112.5}{100} = 1.125 \]

### Step 4: Solve for the original height
Using the equation for height:
\[ 1.125H = 18 \]
To find \( H \), divide both sides by 1.125:
\[ H = \frac{18}{1.125} \]

Calculating this gives:
\[ H = 16 \text{ inches} \]

### Step 5: Solve for the original width
Using the equation for width:
\[ 1.125W = 22.5 \]
To find \( W \), divide both sides by 1.125:
\[ W = \frac{22.5}{1.125} \]

Calculating this gives:
\[ W = 20 \text{ inches} \]

### Step 6: Conclusion
The original dimensions of the image were:
- Height = 16 inches
- Width = 20 inches

Thus, the size of the original image is **16 inches tall by 20 inches wide**.

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