Question

Gabby and Sydney bought some pens (x) and pencils (y) gabby bought 4 pens and 5 pencils she spent$6.71 Sydney bought 5 pens and 3 pencils and paid $7.12 find the cost of each

Answer 1

The cost of pen is $
`1.19`. And cost of pencil is $
`0.39`

Explanation:

Given cost of pen is
`x`.

And cost of pencil is
`y`.

Also, Gabby bought
`4` pens and
`5` pencils, when she spent$
`6.71`

Then, the equation will be

`4x+5y=6.71\ Equation(1)`

And Sydney bought
`5` pens and
`3` pencils and paid $
`7.12`.

Then, the equation will be

`5x+3y=7.12\ Equation(2)`

So,

`3y=7.12-5x\\\\y=((7.12-5x))/(3)`

Plug

`y=((7.12-5x))/(3)` in Equation (1) we get,

`4x+5* ((7.12-5x))/(3)=6.71\\\\4x+1.66(7.12-5x)=6.71\\4x+11.866-8.33x=6.71\\11.866-4.33x=6.71\\11.866-6.71=4.33x\\5.156=4.33x\\x=(5.156)/(4.33)\\x=1.19`

Plug the value of
`x` in Equation (2) we get,

`5x+3y=7.12\\5* 1.19+3y=7.12\\5.95+3y=7.12\\3y=7.12-5.95\\3y=1.166\\y=(1.166)/(3)\\y=0.39`

So, the cost of pen is $
`1.19`. And cost of pencil is $
`0.39`