Question

systems of linear equations: tutorial
continue
lets go back to an example we looked at earlier to solve for the values for the cost of stickers, cards, and markers at the local craft store for brenda, sheena, and cody.
$3s + 4c + 5m = 24.40$
$6s + 5c + 2m = 30.40$
$3s + 2c + m = 13.40$
type the correct answer in each box.
each sheet of stickers, s, costs $____; a box of cards, c, costs $__; and a marker, m, costs $__.

Explanation:

Step1: Label the equations

Let:
Equation 1: $3s + 4c + 5m = 24.40$
Equation 2: $6s + 5c + 2m = 30.40$
Equation 3: $3s + 2c + m = 13.40$

Step2: Eliminate $s$ from Eq1 & Eq3

Subtract Equation 3 from Equation 1:
$(3s + 4c + 5m) - (3s + 2c + m) = 24.40 - 13.40$
$2c + 4m = 11.00$
Simplify: $c + 2m = 5.50$ → Equation 4

Step3: Eliminate $s$ from Eq2 & Eq3

Multiply Equation 3 by 2: $6s + 4c + 2m = 26.80$
Subtract this from Equation 2:
$(6s + 5c + 2m) - (6s + 4c + 2m) = 30.40 - 26.80$
$c = 3.60$

Step4: Solve for $m$ using Eq4

Substitute $c=3.60$ into Equation 4:
$3.60 + 2m = 5.50$
$2m = 5.50 - 3.60 = 1.90$
$m = \frac{1.90}{2} = 0.95$

Step5: Solve for $s$ using Eq3

Substitute $c=3.60$ and $m=0.95$ into Equation 3:
$3s + 2(3.60) + 0.95 = 13.40$
$3s + 7.20 + 0.95 = 13.40$
$3s + 8.15 = 13.40$
$3s = 13.40 - 8.15 = 5.25$
$s = \frac{5.25}{3} = 1.75$

Answer:

Each sheet of stickers, $s$, costs $\$1.75$; a box of cards, $c$, costs $\$3.60$; and a marker, $m$, costs $\$0.95$.