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 14 twin-size blankets and 48 queen-size blankets, using a total of 440 yards of fabric. Last week, the members completed 32 twin-size blankets and 12 queen-size blankets, which required 224 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.

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 14 twin-size blankets and  48 queen-size blankets, using a total of 440 yards of fabric. Last week, the members completed 32 twin-size blankets and  12 queen-size blankets, which required 224 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.

Bytelearn · Accepted Answer

Equations Setup: Let's denote the amount of fabric used for each twin-size blanket as t and for each queen-size blanket as q. We are given that 14 twin-size blankets and 48 queen-size blankets use a total of 440 yards of fabric, which gives us the equation 14t + 48q = 440.Initial Equations: From the previous week, we know that 32 twin-size blankets and 12 queen-size blankets required 224 yards of fabric, which gives us the equation 32t + 12q = 224.Elimination Process: We now have a system of two equations: 1. 14t + 48q = 440 2. 32t + 12q = 224 We will use elimination to solve this system. To eliminate one of the variables, we can multiply the second equation by 4 to match the coefficient of q in the first equation.Variable Elimination: Multiplying the second equation by 4 gives us 128t + 48q = 896. Now we have: 1. 14t + 48q = 440 2. 128t + 48q = 896Solving for t: We subtract the first equation from the second equation to eliminate q. This gives us 114t = 456.Substitute t into Equation: Dividing both sides of the equation 114t = 456 by 114 gives us t = 4. This means that each twin-size blanket uses 4 yards of fabric.Solving for q: Now we substitute t = 4 into the first equation 14t + 48q = 440 to find q. This gives us 14(4) + 48q = 440, which simplifies to 56 + 48q = 440.Subtracting 56 from both sides of the equation 56 + 48q = 440 gives us 48q = 384.Dividing both sides of the equation 48q = 384 by 48 gives us q = 8. This means that each queen-size blanket uses 8 yards of fabric.

Full solution

More problems from Solve a system of equations using elimination: word problems

Related topics