Problem:
Number Concepts-Integers (InterMath)

Jeff had fewer than 100 blocks. When he made five equal rows, he had only one left over; with four equal rows, he had one left over; and with nine equal rows, he had none left over. How many blocks did Jeff have?

 

Solution:

First of all, when we know that with nine equal rows he had none leftover we know that it has to be a multiple of 9.

We begin to solve the problem by writing multiples of 9

9
18
27
36
45

We can cross 45 off because when you divide it by 5 there is no remainder. According to our problem if we have five equal rows we need to have one left over.

54
63
72
81

Divide 81 by 5 and you get a remainder of 1...that works!
Divide 81 by 4 and we get a remainder of 1...that works!
Divide this by 9 and, of course, we get a remainder of 0...this works!

 

Therefore, Jeff has 81 blocks.

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