2qt. of a sugar solution was mixed with 9qt. of a 60% sugar solution to make a 50% sugar solution. Find the percent concentration of the first solution.

Question

can you please explain it step by step mathematically? 

Answer 1

The formula to solve this question is C₁V₁ + C₂V₂ = C₃V₃, where C = Concentration and V = Volume

 

we know that the total volume will be 11qt

 

so. we have 2q x% + 9q 60% = 11q 50%

 

Let's change the percentages to decimals, so 60% = 0.6, and 50% = 0.5

 

our equation becomes 2q x + 9q0.6  =  11q 0.5

expanding, 2qx  + 5.4q = 5.5q

solving, x = ( 5.5q - 5.4q) / 2q

x = 0.05 x 100% = 5%

 

Proof: 2q 0.05 + 9q 0.6 = 11q 0.6; 0.1q + 5.4q = 5.5q