I need help with this word problem

Question

Michael buys 3 notebooks and 4 packages of

highlighters for $12. Amy buys 6 notebooks and

2 packages of highlighters for $15. What is the

cost of one notebook? What is the cost of one

package of highlighters?

Answer 1

We need a bit of algebra to describe simultaneous equations in two unknowns...

let N = Notebooks and H = packs of Highlighters

(1) 3N + 4H = 12

and

(2) 6N + 2H = 15

double (2) and subtract from (1) to eliminate H

3N + 4H = 12

-

12N + 4H = 30

=

-9N + 0H = -18

=> 9N = 18 => N = 2

now substitute N to find H...

3N + 4H = 12

=> 4H = 12 - 3N = 12 - 3(2) = 6

=> H = 1.5

Hence, one notebook costs $2 and one pack of highlighters costs $1.50.

We can double-check 6N + 2H = 6(2) + 2(1.5) = 15 as required.