You want to purchase 2 dozen pencils and a pen. Those items cost $8.45 and you do not have enough money. You decide to purchase 8 fewer pencils and pay $6.05. How much was the pen?

Question

Please explain step by step, or at least how did you get the final answer.

Answer 1

You have 2 unknowns: the cost of 1 pencil and the cost of 1 pen. Therefore, you will need 2 equations to solve this.

Let x = cost of a pencil

y = cost of a pen

Eq. 1: 24x + 1y = 8.45--->y = 8.45 - 24x

Eq. 2: 16x + 1y = 6.05--->y = 6.05 - 16x

Because the "x" and "y" values are the same for both equations, you can write 1 equation and solve for "x":

8.45 - 24x = 6.05 - 16x set equations equal

8.45 - 6.05 - 24x = 6.05 - 6.05 - 16x subtract 6.05 from both sides

2.40 - 24x = -16x result

2.40 - 24x + 24x = -16x + 24x add 24x to both sides

2.40 = 8x result

2.40/8 = 8x/8 divide both sides by 8

0.30 = x result of "x"

You can now put this value for "x" into either equation and solve for "y":

24x + 1y = 8.45 Eq. 1

y = 8.45 - 24x subtract 24x from both sides to isolate the "y" term

y = 8.45 - 24(0.30) substitute for "y" from above

y = 8.45 - 7.20 simplify

y = 1.25 cost for a pen

Therefore, the cost for a pen is $1.25.

Hope this helps!

Answer 2

Use the variable 'a' to be the cost of a pencil, 'b' will be the cost of the pen. Two dozen equals 24, so the first equation can be written:

24a + b = 8.45 ; b = 8.45 - 24a

The second equation involves 24 - 8 pencils, so use 16:

16a + b = 6.05 ; b = 6.05 - 16a

Plug the new value for b into the first equation:

24a + (6.05 - 16a) = 8.45 ; 24a - 16a = 8.45 - 6.05 ; 8a = 2.4 ; a = .3

From this you can see that pencils costs $0.30 apiece. Plus that number into the second equation.

b = 6.05 - (16 x .3) =6.05 - 4.80 = 1.25

Therefore the pen costs $1.25.