Question

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 1 twin bed and 1 queen bed and used a total of 16 pillows. At another house, she used 48 pillows to spruce up 5 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.

Answer 1

By setting up a system of linear equations based on the number of pillows used on twin and queen beds and then utilizing the elimination method, it's determined that the realtor uses 8 pillows on every twin bed and 8 pillows on every queen bed.

Step-by-step explanation:

We need to determine the number of pillows the realtor uses on each twin bed and queen bed by establishing two equations based on the given information. Let's let t represent the number of pillows on one twin bed, and q represent the number of pillows on one queen bed.

From the first house, the equation would be:

1t + 1q = 16

From the second house, the equation would be:

5t + 1q = 48

We have a system of linear equations that can be solved using the substitution or elimination method.

• Solution using the elimination method:
  Write down the system of equations:
• 1t + 1q = 16
• 5t + 1q = 48
• Subtract the first equation from the second to eliminate q:
• This gives us 4t = 32
• Divide both sides by 4 to solve for t:
• t = 8
• Substitute t = 8 back into either equation to solve for q:
• 1(8) + q = 16
• q = 8

So the realtor uses 8 pillows on every twin bed and 8 pillows on every queen bed.