Question

Andrea, Justin, and Virginia went to an office supply store. Andrea bought 6 pencils, 7 markers, and 8 erasers. Her total was $15.75. Justin spent $16.75 buying 6 pencils, 8 markers, and 5 erasers. Virginia bought 5 pencils, 5 markers, and 7 erasers for $11.75. What is the cost of each item?

Answer 1

`x=0.25\,,\,y=1.75\,,\,z=0.25`

Explanation:

Let
`x,y,z` denotes number of pencils, markers, erasers respectively.

For Andrea:

`6x+7y+8z=15.75\,\,\,(i)`

For Justin:

`6x+8y+5z=16.75\,\,\,(ii)`

For Virginia:

`5x+5y+7z=11.75\,\,\,(iii)`

On subtracting equations (i) and (ii), we get

`(6x+7y+8z)-(6x+8y+5z)=15.75-16.75\\-y+3z=-1\\y-3z=1\\y=1+3z`

Put
`y=1+3z` in equation (i)

`6x+7(1+3z)+8z=15.75\\6x+29z=8.75\,\,\,(iv)`

Put
`y=1+3z` in equation (iii)

`5x+5(1+3z)+7z=11.75\\5x+22z=6.75\,\,\,(v)`

Multiply equation (iv) by 5 and equation (v) by 6 and then subtract both the equations.

`5(6x+29z)-6(5x+22z)=5(8.75)-6(6.75)\\13z=3.25\\z=(3.25)/(13)=0.25`

Put
`z=0.25` in equation
`y=1+3z`

`y=1+3(0.25)=1.75`

Put
`y=1.75\,,\,z=0.25` in equation (i)

`6x+7(1.75)+8(0.25)=15.75\\6x+12.25+2=15.75\\6x=1.5\\x=0.25`