Three packs of paper and six markers cost $4.50. Eleven markers and seven packs of paper cost $9.54. How much does one marker cost?

Question

Three packs of paper and six markers cost $4.50. Eleven markers and seven packs of paper cost $9.54. How much does one marker cost?

Answer 1

For this problem, identify the variables:

p = pack of paper

m = marker

 

Then setup the equations:

3p + 6m = $4.50

11m + 7p = $9.54

 

This is a three-step problem:

1. Single out the variable on one side of the first formula
2. Apply the variable (first formula) into the second formula
3. Use the answer from the second formula and apply it to the first formula

 

===

 

3p + 6m = $4.50

3p + 6m - 6m = $4.50 - 6m

3p = $4.50 - 6m

3p ÷ 3 = ($4.50 - 6m) ÷ 3

p = ($4.50 ÷ 3) - (6m ÷ 3)

p = $1.50 - 2m

 

11m + 7p = $9.54

11m + (7 * ($1.50 - 2m) = $9.54

11m + $10.50 - 14m = $9.54

$10.50 - 3m = $9.54

$10.50 - 3m + 3m = $9.54 + 3m

$10.50 = $9.54 + 3m

$10.50 - $9.54 = $9.54 - $9.54 + 3m

$0.96 = 3m

$0.96 ÷ 3 = 3m ÷ 3

$0.32 = m

 

p = $1.50 - 2m

p = $1.50 - (2 * $0.32)

p = $1.50 - $0.64

p = $0.86

 

===

 

So your answer should be 32¢ for one marker

 

To double check the answer, apply the answers you got for the variables into the two formulas.

 

3p + 6m = $4.50

(3 * $0.86) + (6 * $0.32) = $4.50

$2.58 + $1.92 = $4.50

$4.50 = $4.50

11m + 7p = $9.54

(11 * $0.32) + (7 * $0.86) = $9.54

$3.52 + $6.02 = $9.54

$9.54 = 9.54

 

Hope this helps.