Question

Liz and Michael went shopping at an office supply store. Liz bought 3 boxes of pens and 2 notebooks for a total cost of $16.50. Michael bought 2 boxes of the same pens and 1 of the same notebooks for a total cost of $10.25. What is the cost of 1 notebook?

Answer 1

Answer: One notebook costs 2.25 dollars ($2.25)

Step-by-step explanation: To begin with we shall call each box of pen letter p and each notebook we shall call letter n. If Liz bought 3 boxes of pens and 2 notebooks for a total of 16.50 dollars, then this can be expressed as

3p + 2n = 16.5 ----------(1)

Similarly, Michael bought 2 boxes of the same pens and 1 of the same notebook for a total cost of 10.25. This we can express as

2p + n = 10.25 ----------(2)

We can now solve for the pair of simultaneous equations by applying the substitution method. In equation (2), make n the subject of the equation and we shall have

n = 10.25 - 2p

Substitute for the value of n into equation (1)

3p + 2(10.25 - 2p) = 16.5

3p + 20.5 - 4p = 16.5

Collect like terms and we now have

3p - 4p = 16.5 - 20.5

-p = -4

Multiply both sides of the equation by -1

p = 4

Having calculated the value of p, substitute for the value of p into equation (2)

2(4) + n = 10.25

8 + n = 10.25

Subtract 8 from both sides of the equation

n = 2.25

From our calculations one notebook (n) costs $2.25

Answer 2

The cost of 1 notebook is $2.25

Explanation:

First, we assign variables.

Let the cost of a notebook be $n while the cost of a pen be $p

Using Liz’s case, 3 pen boxes and 2 notebooks were bought.

Total cost of this is 3p + 2n = 16.5. •••••••(i)

Using Micheal’s case, 2 pen boxes and 1 notebook

Total cost = 2p + n = 10.25 •••••••(ii)

We now have two equations to solve simultaneously. From ii, n = 10.25 - 2p ; let’s insert this into i

3p + 2(10.25 -2p) = 16.5

3p + 20.5 - 4p = 16.5

4p - 3p = 20.5 - 16.5

p = $4

From the breakaway equation, n = 10.25 - 2p

n = 10.25 - 2(4)

n = 10.25 -8

n = $2.25