146k views
2 votes
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?

User Santrix
by
7.9k points

2 Answers

3 votes

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

User Rburhum
by
8.1k points
2 votes

Answer:

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

User Ed Ballot
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories