Please help with this math word problem:
Jamal has a 5X7 picture that he took on his summer vaction and he wants to use a photo copier to enlarge it to an 8X10 picture. To enlarge Jamal has to specify a percent between 50% and 200% on the copier. Explain 2 different ways Jamal can enlarge the picture to make it an 8X10.
Thank you so very much for helping.
You want to increase the width from 5 to 8 which is an increase of 60%
To prevent distortion, the length would have to be increased by that same percentage, so
1.60(7) = 11.2
BUT, we wanted it to be 10, so you will have to crop the picture.
To find two different ways for Jamal to enlarge his 5x7 picture to an 8x10 picture using the photo copier, we need to consider the aspect ratio of the two sizes.
Aspect ratio is the proportional relationship between the width and height of an image. The aspect ratio of the original 5x7 picture is 5:7, while the aspect ratio of the desired 8x10 picture is 8:10 or 4:5.
Method 1: Maintaining the aspect ratio
One way for Jamal to enlarge his picture while maintaining the aspect ratio is by choosing a specific percentage to scale up both the width and height of the original picture. Here's how to calculate it:
1. Determine the aspect ratio of the original picture: 5:7
2. Determine the aspect ratio of the desired picture: 4:5 (8:10 simplified)
3. Find the scale factor for the width:
Scale factor = (desired width) divided by (original width)
= 8 divided by 5
= 1.6
4. Find the scale factor for the height (using the same ratio as the width):
Scale factor = (desired height) divided by (original height)
= 10 divided by 7
= 1.43
By using the same scale factor for both the width and height, we can ensure that the aspect ratio stays the same. In this case, Jamal needs to specify a 160% enlargement on the photo copier to maintain the aspect ratio and obtain an 8x10 picture.
Method 2: Using different scale factors
Another way for Jamal to enlarge his picture to an 8x10 size is by choosing different scale factors for the width and height. Here's how to calculate it:
1. Determine the aspect ratio of the original picture: 5:7
2. Determine the aspect ratio of the desired picture: 4:5 (8:10 simplified)
3. Find the scale factor for the width:
Scale factor = (desired width) divided by (original width)
= 8 divided by 5
= 1.6
4. Find the scale factor for the height:
Scale factor = (desired height) divided by (original height)
= 10 divided by 7
= 1.43
In this method, the scale factors for the width and height are different. Jamal needs to specify a 160% enlargement for the width (5x1.6=8) and a 143% enlargement for the height (7x1.43=10) on the photo copier.
Both of these methods will result in an 8x10 picture, but they use different scale factors to achieve it.