problem solving

Question

a man ordered 4 times as many boxes of ballpoint pens as boxes of felt-tips.  Ballpoint cost $4.37 per box, Felt-tip $3.42 per box.  if man ordered of pens total $83.60 how many boxes of each pen did he buy?

Answer 1

Start by figuring out what one variable is in terms of the other. 

So say x = # of boxes of ballpoint pens and y = # of boxes of felt-tip pens.

 

Then we can say x = 4y (4 times as many ballpoints as felt-tips)

 

And the other equation can be set up this way:

 

4.37x + 3..42y = 83.60

 

Now doing a quick substitution, we rewrite the equation like this:

 

4.37(4y) + 3.42y = 83.60

17.48y + 3.42y = 83.60

20.90y = 83.60

y = 4

Therefore, x = 16 (4*4)

 

To check, plug in our values of x and y into the second equation

 

4.37 (16) + 3.42 (4) = 83.60

69.92 + 13.68 = 83.60

83.60 = 83.60