Problem:
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?
Solution:
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
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