By coincidence, Brittany's Paint Supplies sold equal quantities of two paint colors yesterday: yellow and blue. All yellow paint comes in 9-liter containers while blue paint is sold in containers of 10 liter. What is the smallest amount of each paint color the store must have sold?
liter
The smallest amount of paint that the store must have sold of both colors would have to be a common multiple of both 9 and 10 liters. The smallest such multiple is 90 liters.
To see why, we can list out some multiples of 9 and 10:
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
We can see that the first common multiple of the two series is 90.
Now, we know that the store sold an equal quantity of yellow and blue paint, so we need to split the 90 liters into two parts such that one part is a multiple of 9 and the other part is a multiple of 10. One way to do this is to split it into 2 parts of 45 liters each, where one part is 5 containers of yellow paint (5 x 9 = 45 liters) and the other part is 4 containers of blue paint (4 x 10 = 40 liters).
So the smallest amount of each paint color the store must have sold is 5 containers of yellow paint (45 liters) and 4 containers of blue paint (40 liters).