question is in description. please help !

Question

Oliver has a box of toy cars, but he is not sure how many he has. If he arranges the cars in groups of four, he has three left over. If he arranges them in groups of 3, he has two left over and there are three left over when he puts them in groups of five. Oliver definitely doesn’t have any more than 30 cars, so how many does he have?

Answer 1

Archie,

 

According to the problem, we know the following:

 

4 groups of cars +3 is equal to 3 groups of cars +2, which is also equal to 5 groups of cars +3.

 

For now, lets ignore the groups of 3 cars and concentrate on the other two.

 

So, we know the following:  4x+3=5z+3

Subtract 3 from both sides, leaving 4x=5z

The only answers that will satisfy both is x=5 and z=4

 

So, 4*5+3=23, and 5*4+3=23

Lastly, we know 3y+2=23

3y=21

y=7

 

So, Oliver has 23 cars.

 

 

Answer 2

If he groups them by 4, he has 3 left over.  This means that he has 4 cars in the first group.  Add the remaining 3.  He has 7 cars in this group.

 

If he groups them by 3, he has 2 left over.  This means that he has 3 cars in the second group.  Add the remaining 2.  He has 5 cars in that in this group.

 

If he groups them by 5, he has 3 left over.  This means he will have 5 cars in the third group.  Add the remaining 3.  He has 8 cars in this group.

 

 

Add the amounts from each group to find out how many cars he has in all.

 

 

7 + 5 + 8 = 20

 

He has 20 cars in all.