Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated 4 twin beds and 1 queen bed and used a total of 34 pillows. At another house, she used 76 pillows to spruce up 4 twin beds and 4 queen beds. How many decorative pillows did the realtor arrange on each bed? The realtor used _____ pillows on every twin bed and _____ pillows on every queen bed.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated 4 twin beds and  1 queen bed and used a total of 34 pillows. At another house, she used 76 pillows to spruce up 4 twin beds and  4 queen beds. How many decorative pillows did the realtor arrange on each bed?  The realtor used _____ pillows on every twin bed and _____ pillows on every queen bed.

Bytelearn · Accepted Answer

Equation Setup: Let's denote the number of pillows on each twin bed as t and the number of pillows on each queen bed as q. In the first house, the realtor used 4 twin beds and 1 queen bed with a total of 34 pillows, which gives us the equation 4t + q = 34.Elimination of Variable: In the second house, the realtor used 4 twin beds and 4 queen beds with a total of 76 pillows, which gives us the equation 4t + 4q = 76.Substitution and Solving: We now have a system of two equations. We need to eliminate one of the variables, t or q. We choose to eliminate q because its coefficients are the same in both equations, which makes it easier to eliminate.Final Solution: To eliminate q, we subtract the first equation from the second equation. This gives us 4t + 4q - (4t + q) = 76 - 34, which simplifies to 3q = 42.We divide both sides of the equation 3q = 42 by 3 to solve for q. This gives us q = 42 / 3, which simplifies to q = 14.We substitute q = 14 into the first equation 4t + q = 34 and solve for t. This gives us 4t + 14 = 34.We subtract 14 from both sides of the equation 4t + 14 = 34 to isolate 4t. This gives us 4t = 34 - 14, which simplifies to 4t = 20.We divide both sides of the equation 4t = 20 by 4 to solve for t. This gives us t = 20 / 4, which simplifies to t = 5.

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