Will ordered 2 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ball point pens cost $3.50 per box, and felt-tip pens cost $4.50. If Will's order of pens totaled $46, how many boxes of each type of pen did he buy?

Question

Will ordered 2 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ball point pens cost $3.50 per box, and felt-tip pens cost $4.50. If Will's order of pens totaled $46, how many boxes of each type of pen did he buy?

2 Answers

Answer Question

Answer 1

Let f represent the number of boxes of felt-tip pens. The total order is
2n(3.50) + n(4.50) = 46
n(2*350 + 4.50) = 46 (factor out n)
n*11.50 = 46 (determine the coefficient of n)
n = 4 (divide by the coefficient of n)

Will ordered 8 boxes of ballpoint pens and 4 boxes of felt-tip pens.

Answer 2

Another simplified (and more day-to-day applicable) way of doing it is to take the ratios and create a 'mandated set' to work through the numbers:

Since there are 2x as many ball point pens as felt tip, and ball point pens cost 3.50 and felt tip 4.50...
1- 3.50 (ball point)
2- 3.50 (ball point)
3- 4.50 (felt tip)
Added together makes $11.50 as a mandated set (a quantity that MUST be purchased together to maintain the ratio of 2:1), then simply divide the final number ($46) by $11.50, and you get 4. You now know that there were 4 boxes of felt tip pens, and double that (8 boxes) of ball point pens.

Heh. I like the easy ways... (^_^)