SOLUTION: ricky has some stickers in a box. if he puts the stickers into bags of 9. he will have no stickers left over. if he puts them into bags of 10, he will have 2 stickers left over. w

Question 1139869: ricky has some stickers in a box. if he puts the stickers into bags of 9. he will have no stickers left over. if he puts them into bags of 10, he will have 2 stickers left over. what is the smallest possible number of stickers in the box?
Can you please help me with this problem.
Thank u
Pls could u make it understandable because me and my child have asked people but people make it too confusing
An equation or anything is fine
Thanks so much and sorry for the bother

Found 3 solutions by Theo, jim_thompson5910, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let the number of stickers in the box be equal to x.

when he puts 9 stickers into each bag, then the number of bags is equal to x / 9 with no stickers left over.

when he puts 10 stickers into each bag, then the number of bags is equal to x / 10 with 2 stickers left over.

since there are no left over stickers when you divide the number of stickers in the box by 9, then the number of stickers in the box has to be a multiple of 9.

that means that the numbers of stickers in the box can be equal to 9 or 18 or 27 or 36 or 45 or 54 or 63 or 72 or 81 or 90 or any other multiple of 9 going up to forever, if need be.

you want, however, to find the smallest number of stickers that can be in the box.

start from 9 stickers in the box and work your way up in multiples of 9 until you get a remainder of 2 when you divide the number of stickers by 10.

9 / 10 = 0 with a remainder of 9.
18 / 10 = 1 with a remainder of 8.
27 / 10 = 2 with a remainder of 7.
36 / 10 = 3 with a remainder of 6.
45 / 10 = 4 with a remainder of 5.
54 / 10 = 5 with a remainder of 4.
63 / 10 = 6 with a remainder of 3.
72 / 10 = 7 with a remainder of 2. ***** this is your solution.

the smallest number of stickers in the box has to be 72.

take 72 and divide it by 9 and you get 8 with no stickers left over.

take 72 and divide it by 10 and you get 7 with 2 stickers left over.

your solution is that the minimum number of stickers in the box has to be 72.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

The tutor @Theo has a great solution. A shortcut is to simply look for any multiple of 9 where the units digit (aka "ones digit") is 2. If a number has a 2 in this location, then that number will divide over 10 to get you a remainder of 2.

Examples of getting a remainder of 2, when we divide values over 10:
32/10 = 3 remainder 2
42/10 = 4 remainder 2
92/10 = 9 remainder 2
72/10 = 7 remainder 2
102/10 = 10 remainder 2
1782/10 = 178 remainder 2

This is a very nice property that allows us to effectively spot the remainder without doing much math at all (some could argue there isn't any math being performed as it's simply just reading off the units digit value). The reason why this property works is because of how the base 10 system is set up.

A number like 72 is really 70+2 = 7*10 + 2. Note how the 7*10 part indicates we basically have 7 groups of 10, and then we have an additional 2 left over.

Or you could think of it like this . The 2/10 refers to a remainder of 2 out of 10. I chose not to reduce the fraction 2/10 so we can see how 72/10 leads to 7 & 2/10.

Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.

            This problem is to be solved by "trial and error" method.

They want you find an integer which is multiple of 9 and gives the remainder of 2 when is divided by 10. The multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72 , . . . O-o-o-p -s ! 72 is ended by 2, hence, it gives the remainder 2 when is divided by 10. So, 72 is your ANSWER.

---------------

When students solve such problems (or start learning on how to solve such problems), it is IMPORTANT to give them
an example (a sample), which words to use, how to combine them and how to express the idea and the solution in shortest,
straightforward, correct and clear logical form.

It is an important part of mathematical education.

Then the hope may exist that the child will love Math, some-when . . .

It is why I wrote my post here.

The opportunity should be given to child to hear "the music of Math".

/\/\/\/\/\/\/

Give your child to read the lesson
    - The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9
from this site.

                Come again soon with similar problems and questions - for your child and for yourself ! !

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