SOLUTION: A student bought 3 boxes of pencils and 2 boxes of pens for $6. He then bought 2 boxes of pencils and 4 boxes of pens for $8. Find the cost of each box of pencils and each box of p

Question 1149918: A student bought 3 boxes of pencils and 2 boxes of pens for $6. He then bought 2 boxes of pencils and 4 boxes of pens for $8. Find the cost of each box of pencils and each box of pens.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

First, a solution by logical reasoning....

Let's change the statement of the problem a bit so that the two purchases are by different students. That will make it easier to describe the method for solving the problem.

So we have

Student A: 3 boxes of pencils and 2 boxes of pens for $6.
Student B: 2 boxes of pencils and 4 boxes of pens for $8.

Student B bought twice as many boxes of pens as student A. So consider a third student C buying twice as much as student A, so that students B and C buy the same numbers of boxes of pens.

Student C: 6 boxes of pencils and 4 boxes of pens for $12.

Now compare the purchases by students B and C. They bought the same number of boxes of pens; student C bought 4 more boxes of pencils than student B, and his cost was $4 more. So each box of pencils costs $1.

Then use the purchases of any one of the three students to find that the cost of each box of pens is $1.50.

Now a typical algebraic solution, which follows the exact same path as the solution above.

[1] the cost of 3 boxes of pencils and 2 boxes of pens is $6
[2] the cost of 2 boxes of pencils and 4 boxes of pens is $8

[3] double the first purchase

[4] compare purchases [2] and [3]

[5] the cost of each box of pencils is $1

[6] substitute [5] into [1]

the cost of each box of pens is $1.50

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