Answer:
The cost of pen is $[tex]1.19[/tex]. And cost of pencil is $[tex]0.39[/tex]
Step-by-step explanation:
Given cost of pen is [tex]x[/tex].
And cost of pencil is [tex]y[/tex].
Also, Gabby bought [tex]4[/tex] pens and [tex]5[/tex] pencils, when she spent$[tex]6.71[/tex]
Then, the equation will be
[tex]4x+5y=6.71\ Equation(1)[/tex]
And Sydney bought [tex]5[/tex] pens and [tex]3[/tex] pencils and paid $[tex]7.12[/tex].
Then, the equation will be
[tex]5x+3y=7.12\ Equation(2)[/tex]
So,
[tex]3y=7.12-5x\\\\y=\frac{(7.12-5x)}{3}[/tex]
Plug
[tex]y=\frac{(7.12-5x)}{3}[/tex] in Equation (1) we get,
[tex]4x+5\times \frac{(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=\frac{5.156}{4.33}\\x=1.19[/tex]
Plug the value of [tex]x[/tex] in Equation (2) we get,
[tex]5x+3y=7.12\\5\times 1.19+3y=7.12\\5.95+3y=7.12\\3y=7.12-5.95\\3y=1.166\\y=\frac{1.166}{3}\\y=0.39[/tex]
So, the cost of pen is $[tex]1.19[/tex]. And cost of pencil is $[tex]0.39[/tex]
