A mixture for purple paint requires blue and red paint in a ratio of 4:5. If 44 gallons of red paint re used, how many gallons of blue neede?

In this problem of ratio, you need to take into consideration as to which part of the ratio is which and which. In this case, the ratio presented would be 4:5. The way the variables are stated in the problem, some might get confused and assign the variables to their convenience, thus committing a mistake. The usual keyword for assigning which is which would be respectively. In this case, it wasn't mentioned because a ratio is already presented. So, blue paint is for 4 and the red paint is for 5. Now proceeding with the problem, when red paint is using 44 gallons, how many gallons of blue paint would be needed?

for easier solving, let's turn them to fractions which then would look like this:

4/5 = x/44

To solve for x, you do the cross multiplication which would make the equation look like this:

5x = 4 x 44

Solve

5x = 176

x = 35.2

So the answer would be 35.2 gallons is needed to be in the right ratio with the 44 gallons of red paint to make a purple paint.