Jamal has a 5" by 7" pictutre thathe took on hisn summer vacation and he wants to use a photo copier to enlarge it to fit in an 8"by 10" picture frame,to enlarge the picture jamal need to specify a percent between 50% and 200% on the copier.explain two differant ways jamal can enlargethe picture to make an 8" by 10" picture.
Here are two different ways Jamal can enlarge his picture to fit in an 8" by 10" picture frame:
Method 1: Enlargement by percent increase
1. Calculate the ratio of the desired dimensions to the current dimensions of the picture frame:
- The width ratio = (8 inches) / (5 inches) = 1.6
- The height ratio = (10 inches) / (7 inches) = 1.43
2. Determine the percent increase needed by averaging the width and height ratios:
- Percent increase = [(width ratio + height ratio) / 2] - 1 = [(1.6 + 1.43) / 2] - 1 = 0.515
3. Specify a percent increase of 51.5% on the copier to enlarge the picture.
Method 2: Enlargement by scale factor
1. Calculate the scale factor needed to increase the dimensions of the picture:
- The width scale factor = (8 inches) / (5 inches) = 1.6
- The height scale factor = (10 inches) / (7 inches) = 1.43
2. Determine the smaller scale factor to ensure the entire picture fits within the new dimensions:
- Smaller scale factor = min(width scale factor, height scale factor) = min(1.6, 1.43) = 1.43
3. Specify a percent increase of 143% on the copier to enlarge the picture.
Both methods will result in enlarging the picture to fit within an 8" by 10" picture frame, with the first method specifically targeting a percent increase and the second method determining the scale factor needed. Jamal can choose either method based on his preference or the available options on the copier.
To enlarge the picture, Jamal needs to determine the percentage by which he should increase the dimensions. Here are two different ways Jamal can enlarge the picture to make it fit an 8" by 10" picture frame:
Method 1: Proportional Enlargement
1. Calculate the ratio of the desired dimensions to the original dimensions.
- Width ratio: 8" / 5" = 1.6
- Height ratio: 10" / 7" = 1.43
2. Determine the smallest ratio of the two dimensions.
- Smallest ratio: 1.43
3. Multiply the smallest ratio by 100 to find the percentage increase.
- Percentage increase: 1.43 * 100 = 143%
4. Jamal can specify a 143% enlargement on the copier to fit the picture into the 8" by 10" frame.
Method 2: Calculating Area Comparison
1. Calculate the area of the original picture.
- Original area: 5" * 7" = 35 sq. inches
2. Calculate the area of the desired picture frame.
- Desired area: 8" * 10" = 80 sq. inches
3. Divide the desired area by the original area to find the area enlargement factor.
- Area enlargement factor: 80 sq. inches / 35 sq. inches ≈ 2.286
4. To find the percentage increase, subtract 1 from the area enlargement factor and multiply by 100.
- Percentage increase: (2.286 - 1) * 100 ≈ 128.6%
5. Jamal can specify approximately a 129% enlargement on the copier to fit the picture into the 8" by 10" frame.
Either of these methods can be used to determine the percentage increase required to enlarge the picture to fit an 8" by 10" picture frame.