Number Concepts-Integers (InterMath)

An art-supply store is selling colored pens in packages of three or five.

If the store shelves these packages in boxes that each hold 142 pens,

how many packages of five pens can a box have?



Total pens= 142

142/5 = 28.4

If you only needed boxes full of 5 pens, your answer would be 28 boxes (having estimated to the round integer).

However, you want all of the pens into boxes to be able to be shipped and you cannot have extra pens (the remainder).

Therefore you must work backwards to a number that can be both divided by 5 and has a difference from 142 of a number that is a multiple of 3.

By looking at the problem you can tell that the lowest number that is multiple of 3 that you can subtract from 142 and leave a good number to divide by 5 is 12.

That will leave you 130 to divide by 5.

Final Answer:
26 boxes of five pens
4 boxes of three pens