Write a system of equations to describe the situation below, solve using any method, 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 2 queen beds and used a total of 42 pillows. At another house, she used 31 pillows to spruce up 4 twin beds and 1 queen bed. 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 any method, 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  2 queen beds and used a total of 42 pillows. At another house, she used 31 pillows to spruce up 4 twin beds and  1 queen bed. 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

Define Variables: Let's define the variables for the number of pillows on each bed type. Let x be the number of pillows on each twin bed, and y be the number of pillows on each queen bed.Write Equations: Write the system of equations based on the given information. For the first house: 4 twin beds and 2 queen beds used a total of 42 pillows. 4x + 2y = 42 For the second house: 4 twin beds and 1 queen bed used a total of 31 pillows. 4x + y = 31Elimination Method: Solve the system of equations using the substitution or elimination method. We will use the elimination method. First, we can multiply the second equation by -2 to eliminate y when we add the equations together. -2(4x + y) = -2(31) -8x - 2y = -62Add Equations: Add the modified second equation to the first equation to eliminate y. (4x + 2y) + (-8x - 2y) = 42 + (-62) 4x - 8x + 2y - 2y = 42 - 62 -4x = -20Solve for x: Solve for x. -4x = -20 x = -20 / -4 x = 5 So, the realtor used 5 pillows on every twin bed.Substitute for y: Substitute the value of x into one of the original equations to solve for y. Using the second equation: 4x + y = 31 4(5) + y = 31 20 + y = 31 y = 31 - 20 y = 11 So, the realtor used 11 pillows on every queen bed.

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