Quinn and derek bought office supplies together. quinn bought 10 packs of paper and 12 boxes of pens for a total cost of $33. derek bought 15 packs of paper and 7 boxes of pens for a total of $27.50. how much was one pack of paper? how much was one box of pens?

The cost of one pack of paper was $0.90 and the cost of one box of pens was $2.00

Step-by-step explanation:

Let

x> the cost of one pack of paper

y---> the cost of one box of pens

we know that

10x+12y=33 > equation A

15x+7y=27.50 ---> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (0.9,2)

see the attached figure

Therefore

The cost of one pack of paper was $0.90

The cost of one box of pens was $2.00

pens = $2

paper = .9

Step-by-step explanation:

p = price of a pack of paper

n =  price of a box of pens

10p + 12n = 33

15p + 7n = 27.50

Multiply the first equation by 3

3(10p + 12n )= 33*3

30p +36n = 99

Multiply the second equation by -2

-2(15p + 7n) = 27.50*-2

-30p -14n = -55

Add the 2 modified equations together

30p +36n = 99

-30p -14n = -55

    22n = 44

Divide each side by 22

22n/22 = 44/22

n =2

Each box of pens is $2

Now we can find the price of the paper

10p + 12n = 33

10p +12(2) = 33

10p +24 =33

Subtract 24 from each side

10p+24-24=33-24

10p = 9

Divide by 10

10p/10 =9/10

p = .9

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions