Devin is a landscaper who needs to prepare different types of grass seed for his customers' yards. Bluegrass seed costs $2.00 per pound, while drought-resistant seed costs $3.00 per pound. If the total cost for both types of grass seed was $68.00 and they weighed a combined total of 25 pounds, how many pounds of bluegrass seed did Devin prepare?
Business · High School · Thu Feb 04 2021
Answered on
To determine the number of pounds of bluegrass seed Devin prepared, we can set up a system of equations based on the given information. Let's denote:
- The number of pounds of bluegrass seed as \( x \). - The number of pounds of drought-resistant seed as \( y \).
From the problem we have two key pieces of information:
1. The total cost for both types of seeds is $68: \( 2x + 3y = 68 \) (because bluegrass seed costs $2.00 per pound and drought-resistant seed costs $3.00 per pound). 2. The combined weight of both types of seeds is 25 pounds: \( x + y = 25 \).
Now we have a system of two equations with two variables:
\[ \begin{align*} 2x + 3y &= 68 \quad \text{(1)} \\ x + y &= 25 \quad \text{(2)} \end{align*} \]
We can solve for one variable in terms of the other using equation (2). Let's solve for \( y \) in terms of \( x \):
\[ y = 25 - x \]
Now we substitute the expression for \( y \) back into equation (1):
\[ 2x + 3(25 - x) = 68 \]
\[ 2x + 75 - 3x = 68 \]
Now, let's combine like terms:
\[ -x + 75 = 68 \]
Subtract 75 from both sides to solve for \( x \):
\[ -x = 68 - 75 \] \[ -x = -7 \]
Divide by -1 to get the value of \( x \):
\[ x = 7 \]
Therefore, Devin prepared 7 pounds of bluegrass seed.