Question

Julie begins counting backwards from 1000 by 2’s and at the same time Tony begins counting forward from 100 by 3’s.  If they count at the same rate, what number will they say at the same time?

Answer 1

To find the number Julie and Tony will say at the same time, we need to find the least common multiple (LCM) of 2 and 3. They will say the same number, 102, after 6 counts.

Step-by-step explanation:

Julie is counting backwards from 1000 by 2's and Tony is counting forward from 100 by 3's. To find the number they will say at the same time, we need to find the least common multiple (LCM) of 2 and 3. The LCM of 2 and 3 is 6. So, they will say the same number after 6 counts.

Since Julie is counting backwards, we need to find the multiple of 6 that is smaller than 1000. 6 goes into 1002 evenly, so after 6 counts, Julie will say 1002.

For Tony, since he is counting forward, we need to find the multiple of 6 that is greater than 100. 6 goes into 102 evenly, so after 6 counts, Tony will say 102.

Therefore, Julie and Tony will say the same number, 102, after 6 counts.