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.
To solve this math word problem, Jamal wants to enlarge a 5X7 picture to make it an 8X10 picture. There are two different ways Jamal can do this by specifying a percent between 50% and 200% on the copier.
Method 1: Increasing the dimensions proportionally
One way Jamal can enlarge the picture is by increasing the dimensions proportionally. To achieve this, he can use the concept of ratios.
Step 1: Calculate the ratio of the width and height of the original picture to the desired picture.
- The ratio of the width: 5 / 8 = 0.625
- The ratio of the height: 7 / 10 = 0.7
Step 2: Choose a percent between 50% and 200% by multiplying the ratios calculated in Step 1.
- Let's say Jamal chooses 150% (1.5) as the desired enlargement.
Step 3: Multiply the original dimensions by the chosen percent.
- New width: 5 * 1.5 = 7.5
- New height: 7 * 1.5 = 10.5
Since the picture cannot have a fraction of a dimension, Jamal can round the new dimensions up or down to ensure they are whole numbers. In this case, since the nearest whole numbers are 8 and 11, Jamal can enlarge the picture to 8X11.
Method 2: Using a different ratio for the width and height
Another way Jamal can enlarge the picture is by using a different ratio for the width and height. This method allows for more flexibility in choosing the enlargement percentage.
Step 1: Calculate the ratio of the width and height of the original picture to the desired picture.
- The ratio of the width: 5 / 8 = 0.625
- The ratio of the height: 7 / 10 = 0.7
Step 2: Choose a different percent for the width and height. Let's say Jamal wants to increase the width by 100% (2 times) and the height by 150% (1.5 times).
Step 3: Multiply the original dimensions by the chosen percent for each dimension.
- New width: 5 * 2 = 10
- New height: 7 * 1.5 = 10.5
Again, Jamal needs to round the new dimensions to whole numbers. In this case, rounding down gives 10 for the width and 11 for the height, resulting in an 8X10 enlargement.
Overall, there are multiple ways Jamal can enlarge the picture to make it an 8X10 by specifying a percent between 50% and 200% on the copier. He can either increase the dimensions proportionally or use different ratios for the width and height. The specific method and chosen enlargement percentage will determine the final dimensions of the new picture.