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

Answer:

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

Step-by-step 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,

$3y=7.12-5x\\\\y=\frac{(7.12-5x)}{3}$

Plug

$y=\frac{(7.12-5x)}{3}$ in Equation (1) we get,

$4x+5\times \frac{(7.12-5x)}{3}=6.71\\\\4x+1.66(7.12-5x)=6.71\\4x+11.866-8.33x=6.71\\11.866-4.33x=6.71\\11.866-6.71=4.33x\\5.156=4.33x\\x=\frac{5.156}{4.33}\\x=1.19$

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

$5x+3y=7.12\\5\times 1.19+3y=7.12\\5.95+3y=7.12\\3y=7.12-5.95\\3y=1.166\\y=\frac{1.166}{3}\\y=0.39$

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