Math Problem of the Week - Algebra and Up - May 1, 2022 to May 7, 2022

Algebra and Up: 

Question: Mia has two cans of purple paint and a can of white paint. One of the purples is 30% red and 70% blue. The other is 50% red and 50% blue. If Mia wants 8 fluid ounces of a mixture that is 20% red, 30% blue, and 50% white, how many fluid ounces of each kind of paint does she need? 

Answer:  2 fluid ounces of 30% / 70%, 2 fluid ounces of 50% / 50%, and 4 fluid ounces of white.

Solution:  We know right off the bat that we need 4 ounces of white paint because 50% of 8 ounces is 4 ounces. So, next we need to find out what amounts of the two purple paints to mix together to make 4 ounces of a 40% red, 60% blue paint (we need to double the percentages because we’re only dealing with the half that isn’t white). We can see that the average of 30% red and 50% red is 40% red, so we need equal parts of the first and second paints. That’s 2 ounces of each to make 8 ounces total. Alternatively, we could use the equation 50%(4-x) + 30%x = 4(40%) wherein x represents the amount of the first paint.