An image is 16 in. by 20 in. You want to make a copy that is similar. Its longer side will be 38 in. The copy costs $6.00 per square inch. Estimate the copy's toal cost. Explain.
To estimate the total cost of making a copy of an image, we need to calculate the area of the copy and multiply it by the cost per square inch. Here are the steps to calculate the estimated cost:
1. Determine the longer side of the copy:
- The longer side of the copy is given as 38 inches.
2. Determine the ratio between the longer sides of the original image and the copy:
- The longer side of the original image is 20 inches.
- The ratio is 38/20 = 1.9.
3. Calculate the corresponding length of the shorter side of the copy:
- The original image has shorter side 16 inches.
- Multiply the shorter side by the ratio to find the corresponding length: 16 * 1.9 = 30.4 inches.
4. Calculate the area of the copy:
- To calculate the area, multiply the longer side by the shorter side: 38 * 30.4 = 1155.2 square inches.
5. Determine the total cost:
- The cost per square inch is given as $6.00.
- Multiply the area of the copy by the cost per square inch: 1155.2 * $6.00 = $6931.20.
Therefore, using these calculations, the estimated total cost of making the copy would be approximately $6931.20.
To estimate the copy's total cost, we need to determine the area of the copy first.
Given that the original image is a rectangle with dimensions 16 inches by 20 inches, we can find its area by multiplying the length and width:
Area of the original image = 16 in × 20 in = 320 square inches
Since the copy is similar to the original, we know that the ratios of corresponding sides will be equal. We are given that the longer side of the copy is 38 inches, but we don't know the length of the shorter side. However, we can determine the ratio by dividing the longer side of the copy by the corresponding longer side of the original image:
38 in / 20 in = 1.9
Now, let's find the length of the shorter side of the copy by multiplying this ratio by the shorter side of the original image:
1.9 × 16 in = 30.4 inches
So, the dimensions of the copy are approximately 30.4 inches by 38 inches.
To estimate the total cost, we need to calculate the area of the copy:
Area of the copy = 30.4 in × 38 in = 1155.2 square inches
Given that the cost of the copy is $6.00 per square inch, we can multiply the area of the copy by the cost per square inch:
Total cost = 1155.2 square inches × $6.00/square inch = $6931.20
Therefore, the estimated total cost of the copy is $6931.20.
Y = 16/20 * 38 = 30.4 in. = Length of
short side.
Cost = 6*Area = 6 * (38*30.4) =
20/16 = 38/30.4 = 1.25