Question

Quinn and Derek bought office supplies together. Quinn bought 10 packages of paper and 12 boxes of pens for a total cost of $ 33. Derek bought 15 packages of paper and 7 boxes of pens for a total of $ 27.5o. How much did a paper package cost? How much did a bunch of pens cost?

Answer 1

The cost of one package of paper is $0.90 and one box of pens costs $2.00, which was determined by setting up and solving a system of linear equations.

Step-by-step explanation:

To solve the problem where Quinn and Derek buy office supplies together, we need to set up a system of linear equations based on the information provided:

1. Quinn bought 10 packages of paper and 12 boxes of pens for a total cost of $33.
2. Derek bought 15 packages of paper and 7 boxes of pens for a total cost of $27.50.

Let the cost of one package of paper be represented by x dollars and the cost of one box of pens be represented by y dollars. Using the information given, we can write the following equations:

1. 10x + 12y = 33
2. 15x + 7y = 27.50

Multiplying the first equation by 15 and the second equation by 10, we can eliminate x when we subtract the second equation from the first:

1. (15)(10x + 12y) = (15)(33)
2. (10)(15x + 7y) = (10)(27.50)

We get:

1. 150x + 180y = 495
2. 150x + 70y = 275

Subtracting the second equation from the first:

110y = 220

Dividing both sides by 110, we find that:

y = 2

Substituting y = 2 into the first original equation 10x + 12y = 33, we get:

10x + 24 = 33

Subtracting 24 from both sides:

10x = 9

And dividing both sides by 10, we find that:

x = 0.9

Therefore, the package of paper costs $0.90 and the box of pens costs $2.00.