# Math

posted by .

Maxie counted her dimes,when she put them in a groups of 4 she had 2 left over, groups of 5 1 left over. What is the smallest number of dimes she could have over if she has more than 10

• Math -

You are looking for the smallest number N that satisfies
N mod 4 = 2, ....(1)
N mod 5 = 1 .....(2)

Since N mod 4 = 2 can only be satisfied by an even number, N can only be a number that ends in the digit 6 if (2) is to be satisfied.
Since it is over 10, and 16 does not satisfy (1), we choose 26 as the smallest number over 10 that satisfies the two given conditions.

For a formal treatment of this class of problems, look up the "Chinese remainder theorem".

## Similar Questions

1. ### Math

I'm having alot of problems with the problem. I don't want the answer but I need to know how to figure it out to get the answer. To put it in another way I don't know where to start. A farmer takes to market in her cart, but she hit …

Mazie counted her dimes. When she put them in groups of 4, she had 2 left over. When she put them in groups of 5, she had one left over. What is the smallest number of dimes she could have, if she has more than 10
3. ### algebra

a farmer is taking her eggs to market in her cart, but she hits a pothole, whick knocks over all the containers of eggs. Though she herself is unhurt, every egg is broken. So she goes to the insurance agent who asks her how many eggs …
4. ### math

I am a 2-digit number over 50. When you put me in groups of 7, two are left over. The sum of my digits is 11. What number am I?
5. ### Math

Maize counted her dime.when she put them in groups of 4 ,she had two dimes left over.when she put them in group of 5,she had one left over.what is the smallest number of dimes she could have.if she has more than 10?
6. ### Maths

marie puts dimes in groups of 4 with 2 dimes left over. When she puts them in groups of 5, she had 1 left over?
7. ### Math 1350

When Mike sorts his marbles, he notices that if he put them in groups of 5, he has one left over. When he sorts them in groups of 7, he also has one left over, but in groups of 6, he has none left over. What is the smallest number …
8. ### Math

Abel Save a 43 more nickels than dimes. After he spents 17 dimes, he had twice as many nickel than dimes . How many coins did he have left ?
9. ### math

Abel Save a 43 more nickels than dimes. After he spents 17 dimes, he had twice as many nickel than dimes . How many coins did he have left ?
10. ### Algebra

You are playing with a pile of beads and notice if you put them in groups of 4 you have 3 beads left over, in groups of 5 you have 4 beads left over and in groups of nine you do not have any left over. What is the smallest number of …

More Similar Questions