Question

gabby and sydney bought some pens and pencils. gabby bought 4 pens and 5 pencils for $6.71. sydney bought 5 pens and 3 pencils for $7.12. find the cost of each. (select 2)

Explanation:

Step1: Define variables for costs

Let $p$ = cost of 1 pen (in dollars), $c$ = cost of 1 pencil (in dollars).

Step2: Set up system of equations

From Gabby's purchase: $4p + 5c = 6.71$
From Sydney's purchase: $5p + 3c = 7.12$

Step3: Eliminate one variable (scale equations)

Multiply first equation by 3: $12p + 15c = 20.13$
Multiply second equation by 5: $25p + 15c = 35.60$

Step4: Subtract equations to solve for $p$

Subtract scaled first equation from scaled second:
$$(25p + 15c) - (12p + 15c) = 35.60 - 20.13$$
$$13p = 15.47$$
$$p = \frac{15.47}{13} = 1.19$$

Step5: Substitute $p$ to find $c$

Plug $p=1.19$ into $4p + 5c = 6.71$:
$$4(1.19) + 5c = 6.71$$
$$4.76 + 5c = 6.71$$
$$5c = 6.71 - 4.76 = 1.95$$
$$c = \frac{1.95}{5} = 0.39$$

Answer:

Cost of one pen: $\$1.19$, Cost of one pencil: $\$0.39$