Question

Denis has bought box of pens and pencils . He has paid $450 for 27 boxes together. The pen box is $15 and the pencil box is $18. How many of each box has Denis got?

Select one:

a. 17 pens and 10 pencils

b. 12 pencils and 15 pens

c. 12 pens and 15 pencils

d. 10 pens and 17 pencils

Answer 1

c. 12 pens and 15 pencils

Explanation:

We can find the number of each box Denis bought using a system of equations.

Let x represent the number of pen boxes and y the number of pencil boxes Denis bought

First equation:

We know that the sum of the quantities of the pen and pencil boxes equals the total number of boxes altogether as

# of pen boxes + # of pencil boxes = total number of boxes

x + y = 27

Second equation:

We know that the sum of the costs of the pen and pencil boxes equals the total cost as

(price of pen boxes * # of pen boxes) + (price of pencil boxes * # of pencil boxes) = total cost

15x + 18y = 450

Method to solve: Substitution:

We can isolate x in the first equation and plug it in for x in the second equation. This will allow us to first find y:

(x + y = 27) - y

x = -y + 27

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15(-y + 27) + 18y = 450

-15y +405 + 18y = 450

3y + 405 = 450

3y = 45

y = 15

Find x:

Now we can find x by plugging in 15 for y in x + y = 27:

x + 15 = 27

x = 12

Thus, Denis bought 15 pens and 12 pencils (answer choice c.)

Check work:

We can check our work by plugging in 15 for y and 12 for x in both equations and seeing if we get 27 for the first equation and 450 for the second equation:

Checking solutions in x + y = 27:

12 + 15 = 27

27 = 27

Checking solutions in 15(12) + 18(15) = 450

15(12) + 18(15) = 450

180 + 270 + 450

450 = 450

Thus, our answers are correct.