Jasmine paid $10 for 5/8 yard of fabric to make a pillow. She wants t know the price of 4 yards of the same fabric so that she can make a quilt
The correct answer and explanation is:
Let’s solve the problem step by step.
Problem:
Jasmine paid $10 for 5/8 yard of fabric. She wants to find out the cost for 4 yards of the same fabric.
Step 1: Find the price per yard
- Jasmine paid $10 for 5/8 yard.
- To find the price per 1 yard, we divide $10 by (5/8):
Price per yard=1058=10×85=805=16\text{Price per yard} = \frac{10}{\frac{5}{8}} = 10 \times \frac{8}{5} = \frac{80}{5} = 16
So, the price per yard is $16.
Step 2: Calculate the price for 4 yards
- Now that we know 1 yard costs $16, multiply by 4 yards:
Cost for 4 yards=4×16=64\text{Cost for 4 yards} = 4 \times 16 = 64
So, 4 yards of fabric will cost $64.
Explanation:
When Jasmine bought the fabric, she paid $10 for a portion that was less than a full yard — specifically, 5/8 of a yard. To find out how much 1 full yard costs, we use the unit rate method. Dividing the total price by the fraction of the yard purchased tells us the price of one full yard.
Mathematically, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 5/8 is 8/5. So, $10 divided by 5/8 becomes $10 × 8/5, which equals $16.
Once we know the price per yard, we multiply it by the number of yards Jasmine wants to buy for her quilt (4 yards). Multiplying $16 × 4 gives us $64.
Thus, Jasmine should expect to pay $64 for 4 yards of the same fabric.