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 44 twin-size blankets and 35 queen-size blankets, using a total of 526 yards of fabric. Last week, the members completed 23 twin-size blankets and 35 queen-size blankets, which required 442 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 44 twin-size blankets and  35 queen-size blankets, using a total of 526 yards of fabric. Last week, the members completed 23 twin-size blankets and  35 queen-size blankets, which required 442 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

Denote Fabric Usage Equations: Let's denote the amount of fabric used for each twin-size blanket as t and for each queen-size blanket as q. We have two weeks of data, which gives us two equations. The first week's production of 44 twin-size and 35 queen-size blankets using 526 yards of fabric gives us the equation 44t + 35q = 526. Week 1 Production Data: The second week's production of 23 twin-size and 35 queen-size blankets using 442 yards of fabric gives us the equation 23t + 35q = 442. System of Equations: We now have a system of two equations with two variables: 1. 44t + 35q = 526 2. 23t + 35q = 442 We will use elimination to solve for t and q. To eliminate q, we can subtract the second equation from the first.Elimination Method: Subtracting the second equation from the first, we get: (44t + 35q) - (23t + 35q) = 526 - 442 This simplifies to 21t = 84.Subtract Equations: Dividing both sides of the equation 21t = 84 by 21, we find that t = 4. This means that each twin-size blanket uses 4 yards of fabric.Solve for t: Now that we know the value of t, we can substitute it back into one of the original equations to solve for q. We'll use the second equation: 23t + 35q = 442. Substituting t = 4, we get 23(4) + 35q = 442.Substitute t into Equation: Calculating the first term, we have 23 * 4 = 92, so the equation becomes 92 + 35q = 442.Calculate for q: Subtracting 92 from both sides of the equation 92 + 35q = 442, we get 35q = 350.Final Fabric Usage Results: Dividing both sides of the equation 35q = 350 by 35, we find that q = 10. This means that each queen-size blanket uses 10 yards of fabric.We have found that a twin-size blanket uses 4 yards of fabric and a queen-size blanket uses 10 yards of fabric.

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