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?

Question

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Respuesta :

berno berno · Answer 1 · 2020-02-20T10:08:10+01:00

Answer:

[tex]x=0.25\,,\,y=1.75\,,\,z=0.25[/tex]

Step-by-step explanation:

Let [tex]x,y,z[/tex] denotes number of pencils, markers, erasers respectively.

For Andrea:

[tex]6x+7y+8z=15.75\,\,\,(i)[/tex]

For Justin:

[tex]6x+8y+5z=16.75\,\,\,(ii)[/tex]

For Virginia:

[tex]5x+5y+7z=11.75\,\,\,(iii)[/tex]

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

[tex](6x+7y+8z)-(6x+8y+5z)=15.75-16.75\\-y+3z=-1\\y-3z=1\\y=1+3z[/tex]

Put [tex]y=1+3z[/tex] in equation (i)

[tex]6x+7(1+3z)+8z=15.75\\6x+29z=8.75\,\,\,(iv)[/tex]

Put [tex]y=1+3z[/tex] in equation (iii)

[tex]5x+5(1+3z)+7z=11.75\\5x+22z=6.75\,\,\,(v)[/tex]

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

[tex]5(6x+29z)-6(5x+22z)=5(8.75)-6(6.75)\\13z=3.25\\z=\frac{3.25}{13}=0.25[/tex]

Put [tex]z=0.25[/tex] in equation [tex]y=1+3z[/tex]

[tex]y=1+3(0.25)=1.75[/tex]

Put [tex]y=1.75\,,\,z=0.25[/tex] in equation (i)

[tex]6x+7(1.75)+8(0.25)=15.75\\6x+12.25+2=15.75\\6x=1.5\\x=0.25[/tex]