Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The members of a sewing circle are making blankets to give to shelters. This week, they made 36 twin-size blankets and 34 queen-size blankets, using a total of 342 yards of fabric. Last week, the members completed 36 twin-size blankets and 17 queen-size blankets, which required 189 total yards of fabric. How much fabric is used for the different sizes of blankets? A twin-size blanket uses yards of fabric and a queen-size one uses yards.

Answer 1

Let's denote the number of yards of fabric used for a twin-size blanket as

�

T and for a queen-size blanket as

�

Q.

The system of equations based on the information given is as follows:

For this week:

Equation 1:

36

�

+

34

�

=

342

Equation 1:

​

36T+34Q=342

​

For last week:

Equation 2:

36

�

+

17

�

=

189

Equation 2:

​

36T+17Q=189

​

Now, let's solve this system using the elimination method. Subtracting Equation 2 from Equation 1 to eliminate

�

T:

(

36

�

+

34

�

)

−

(

36

�

+

17

�

)

=

342

−

189

17

�

=

153

�

=

153

17

�

=

9

​

(36T+34Q)−(36T+17Q)=342−189

17Q=153

Q=

17

153

​

Q=9

​

Now that we have the value for

�

Q, we can substitute it back into either Equation 1 or 2. Let's use Equation 1:

36

�

+

34

(

9

)

=

342

36

�

+

306

=

342

36

�

=

36

�

=

1

​

36T+34(9)=342

36T+306=342

36T=36

T=1

​

Therefore, a twin-size blanket uses 1 yard of fabric, and a queen-size blanket uses 9 yards of fabric.