Question

the manager of a garden shop mixes grass seed that is 35% rye grass with 60 lb of grass seed that is 60% rye grass to make a mixture that is 53% rye grass. how much of the 35% rye grass is used?

Explanation:

Step1: Set up the equation

Let $x$ be the amount (in pounds) of the 35% rye - grass seed. The amount of rye - grass in the 35% seed is $0.35x$, the amount of rye - grass in the 60 - lb of 60% seed is $0.6\times60$, and the total amount of the mixture is $(x + 60)$ lb with 55% rye - grass, so the amount of rye - grass in the mixture is $0.55(x + 60)$. Then the equation is $0.35x+0.6\times60=0.55(x + 60)$.

Step2: Expand and simplify the equation

First, expand the right - hand side: $0.35x + 36=0.55x+33$.

Step3: Solve for $x$

Subtract $0.35x$ from both sides: $36 = 0.55x-0.35x + 33$.
Simplify the right - hand side: $36=0.2x + 33$.
Subtract 33 from both sides: $0.2x=36 - 33=3$.
Divide both sides by 0.2: $x=\frac{3}{0.2}=15$.

Answer:

15 lb