Question

the cost of 4 boxes of pens and 3 boxes of pencils is $22.55. the cost of 3 boxes of pens and 2 boxes of pencils is $16.45. find the cost of both. (select 2) $2.75 $4.25 $2.15 $3.35 $1.95

Explanation:

Step1: Define variables

Let $x$ = cost of 1 pen box, $y$ = cost of 1 pencil box.

Step2: Set up equations

$$4x + 3y = 22.55$$
$$3x + 2y = 16.45$$

Step3: Eliminate $y$ (scale equations)

Multiply first eq by 2: $8x + 6y = 45.10$
Multiply second eq by 3: $9x + 6y = 49.35$

Step4: Subtract equations

$(9x + 6y) - (8x + 6y) = 49.35 - 45.10$
$x = 4.25$

Step5: Solve for $y$

Substitute $x=4.25$ into $3x + 2y = 16.45$:
$3(4.25) + 2y = 16.45$
$12.75 + 2y = 16.45$
$2y = 16.45 - 12.75 = 3.70$
$y = \frac{3.70}{2} = 1.85$

Answer:

$4.25, $1.85