Question

Bailey, Jeremiah, and Maggie are buying school supplies. Bailey buys 2 pens and 6 pencils and spends a total of $7.00. Jeremiah buys 3 pens and 5 pencils and spends a total of $7.50. How much will Maggie spend to purchase 4 pens? *
3 points

Answer 1

Explanation:

Here we have to solve a system of linear equations in three variables. Let:

x: Cost of pens

y: Cost of pencils

We know that:

• Bailey buys 2 pens and 6 pencils and spends a total of $7.00. So:

$2x+6y=7 \ ... \ eq1$

• Jeremiah buys 3 pens and 5 pencils and spends a total of $7.50. So:

$3x+5y=7.5 \ ... \ eq2$

Multiplying eq1 by 3 and eq 2 by -2:

$\bullet \ 3(2x+6y)=3(7) \\ \\ 6x+18y=21 \\ \\ \\ \bullet \ -2(3x+5y)=-2(7.5) \\ \\ -6x-10=-15$

Then adding these two resultant equations:

$6x+18y=21 \\ \\ -6x-10y=-15 \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ \\ 8y=6 \\ \\ y=0.75 \\ \\ \\ So \ from \ eq \ 1: \\ \\ 2x+6(0.75)=7 \\ \\ 2x=7-4.5 \\ \\ 2x=2.5 \\ \\ x=1.25$

How much will Maggie spend to purchase 4 pens?

Each pen costs $1.24, so 4 pens will cost:

$\text{Cost of 4 pens}=4(1.25)=\boxed{\ 5}$