Question

2 boxes of pens and 6 boxes of pencils cost $14.00. 4 boxes of pens and 3 boxes of pencils cost 14.50. What is the cost of each box of pencils? Come up with a system of equations to solve.

Answer 1

Using elimination first can help rather than substitution

Answer 2

Lets multiply the first equation by -3
giving us

-3(2b + 6p) = (14 * (-3)
-6b - 18p = 42

Now the second equation by 2
2 (3b + 4p) = 14.50 (2)

6b + 8p = 29

Answer 3

Okay. This is a classic example of simultaneous equations.

We're using 'i' for (ink, to represent pens), and 'g' for graphite, to represent pencils.

2i + 6g = 14

That's your first sentence in mathematical form. Now, we put the next one into graphical form as well.

4i + 3g = 14.5

So, we'll half the top equation and find out what one box of pens is equal to.

i + 3g = 7. Let's find out what pens alone are equal to by rearranging it.

i = 7 - 3g.

Now, we can put this into the other equation, if we know the price of pens.

4(7 - 3g) + 3g = 14.5

28 - 12g + 3g = 14.5

28 - 9g = 14.5

Rearrange it for 13.5 = 9g

Divide each side by 9, and we have one box of pencils costing 1.5.

Now we know that g = 1.5, we can put it back into the original equation.

2i + 6g = 14

2i + 6*1.5 = 14

2i + 9 = 14

2i = 5

i = 2.5

SO, a box of pens costs $2.50, and a box of pencils costs $1.50