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?
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
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.
Divide 81 by 5 and you get a remainder of 1...that
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
Therefore, Jeff has 81 blocks.