Question

Betty an her daughter collect needlepoint throw pillows with silly little sayings on them such as Happy as a Gopher in Soft Dirt. On a recent shopping trip, Betty paid a total of $265 for 2 small needlepoint pillows and 5 large ones. Her daughter loved these very same pillows even more, so she spent a total of $635 on 7 of the small ones and 11 of the large ones. How much did the small pillow cost? How much did the large pillow cost?

Answer 1

the small pillows costed $20 and the large pillows costed $45

Explanation:

this can be set up were x= price of small pillows and y=price of large pillows

according the the question, 265=2x+5y and 635=7x+11y

so now solve this system of equations:

first solve 265=2x+5y for x

add -2x to both sides

-2x+265=5y

add -265 to both sides

-2x=5y-265

divide both sides by -2

x=(-5/2)y+(265/2)

substitute this value of x in 635=7x+11y and solve for y

635=7((-5/2)y+(265/2)) +11y

y=45

substitute 45 for y in x=(-5/2)y+(265/2)and solve for x

x=20

so the small pillows are $20 and the large are $45