The Paint Problem
Sally goes to the paint store to buy some paint. She finds six different kinds of paint but they all have mystery tags on them. This means that she has to use math to find the prices of them. Can you help Sally out?
Red Paint + Blue Paint = $32
Blue Paint + Green Paint = $28
Green Paint + Orange Paint = $30
Orange Paint + Yellow Paint = $32
Yellow Paint + Purple Paint = $40
Red Paint + Green Paint = $36
Blue Paint + Orange Paint = $26
Yellow Paint + Green Paint = $34
Purple Paint + Orange Paint = $36
Add each color of paint together to find your answer!
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Method 1: We have R + B = 3 2 and B + G = 2 8 , so R − G = 4 . Also R + G = 3 6 ; so R = 2 0 , G = 1 6 and B = 1 2 . With these values it's easy to find the others; O = 1 4 , Y = 1 8 , P = 2 2 , giving the total 1 0 2 .
Method 2: ( R + B ) + ( B + G ) − ( G + O ) + ( Y + P ) + 2 ( R + G ) + ( B + O ) + ( Y + G ) + 2 ( P + O ) 3 ( R + B + G + O + Y + P ) R + B + G + O + Y + P = 3 2 + 2 8 − 3 0 + 3 2 + 4 0 + 2 × 3 6 + 2 6 + 3 4 + 2 × 3 6 = 3 0 6 = 1 0 2