Question

Mason spent $15.85 for 3 notebooks and 2 boxes of markers. The boxes of markers cost $3.95 each, and the sales tax was $1.23. Mason also used a coupon for $0.75 off his purchase. If each notebook had the same cost, how much did each notebook cost?

Answer 1

Solving for the cost of each notebook?
Step 1: You need a variable to represent the notebooks so let used z. It doesn't matter the letter could be x , y , z.
We have 3 notebooks so, 3z (notebooks) will be used when we set up the equation.

We see 2 boxes of markers @ $3.95 each, so 2( 3.95) is our markers.

Problem: 3z + 2(3.95) = $15.85 amount spent w/ taxes

Step 2: Subtract taxes and discount coupon from total amount spend.
15.85 - 1.23 (w/taxes) = $14.62
14.62 - .75 (coupon used) = $13.87

New equation: (without coupons and taxes)

Multiple 2 x 3.95 markers 3z + 2(3.95)= 13.87
3z+7.90 = 13.87
Subtract:(7.90) form both sides -7.90 -7.90
3z = 5.97
Divide 3 from both sides 3 3
z is cost of each notebook z = $1.99 (cost each notebook)

Check: Multiply 3(1.99) + 2(3.95) + .75(coupon) + 1.23 taxes= $15.85
Add amounts 5.97 + 7.90 + .75 + 1.23 = $15.85
13.87 + .75 + 1.23 = $15.85
14.62 + 1.23 = $15.85
Correct solution both are equal: $15.85 = $15.85

Answer 2

Let X be the cost of 1 notebook and Y be the cost of 1 box of markers.

The presented information gives us the equations:
3X + 2Y = $14.62 (14.62 is the total cost of 15.85 minus the sales tax of 1.23)
Y = 3.95

Plug the value of Y in the second equation into the first equation to get:
3X + 2(3.95) = 14.62

Simplify and solve for X:
3X + 7.9 = 14.62
3X = 6.72
X = 2.24

The cost of each notebook is $2.24