Question

Two students are going to the store to buy school supplies for the new school year. One of the students buys 2 packs of pencils and 3 packs of pens for $8.25. Her friend purchases 5 packs of pencils and 2 packs of pens for $11.00. Is there enough information to determine the cost of 1 pack of pencils and 1 pack of pens? Explain why or why not.

Answer 1

Yes, it's enough information

Explanation:

yes, there is enough information to determine the cost of 1 pack of pencils and 1 pack of pens

we just need an algebra of elimination and substition to find the coat of each. like this:

pencils = C

pen = N

2 C + 3 N = 8.25 (times by 2)

5 C + 2 N = 11.00 (times by 3)

------------------------- - (we eliminate the N)

4 C + 6 N = 16.50

15 C + 6 N = 33.00

------------------------- -

-11 C = - 16.5

C = (-16.5) : (-11) = $ 1.50

so the price of 1 pack of pencils is $ 1.50

now we use subtitution to find the price of 1 pack of pens

2 C + 3 N = 8.25

2 (1.50) + 3 N = 8.25

3.00 + 3 N = 8.25

3 N = 8.25 - 3.00

3 N = 5.25

N = 5.25 : 3 = $ 1.75

so the price of 1 pack of pencils is $ 1.75