Question

Arliss has two pieces of carpet runner. One is 2/13 yards long and the other is 3/13 yards long. She needs 10 yards of carpet runner altogether. How much more does she need to buy?

a) 19/13 yards
b) 22/13 yards
c) 26/13 yards
d) 31/13 yards

Answer 1

Arliss needs to buy an additional 125/13 yards, or 31/13 yards, of carpet runner to have a total of 10 yards. She already has 5/13 yards from two pieces.

Step-by-step explanation:

The total length of carpet runner that Arliss already has can be determined by adding the lengths of the two pieces she has:

2/13 yards

3/13 yards

Adding these two lengths together, we get:

2/13 + 3/13 = 5/13 yards

To calculate the additional length needed, we subtract the total length Arliss has from 10 yards, which is the total length she needs.

10 yards - 5/13 yards

First, convert 10 yards to 13/13 yards to have a common denominator:

10 yards = (10 x 13)/13 = 130/13 yards

Now, subtract the length of the carpet runner Arliss has:

130/13 yards - 5/13 yards = 125/13 yards

Therefore, Arliss needs to buy 125/13 yards of additional carpet runner, which is equivalent to option d) 31/13 yards.