Question

a lumber company combined oak wood chips that cost $3.30 per pound with pine wood chips that costs $2.20 per pound. how many pounds of each were used to make a 55 - pound mixture costing $2.40 per pound? oak chips lb pine chips lb

Explanation:

Step1: Let variables

Let $x$ be the pounds of oak wood - chips. Then the pounds of pine wood - chips is $55 - x$.

Step2: Set up cost - equation

The cost of the oak wood chips is $3.3x$, the cost of the pine wood chips is $2.2(55 - x)$, and the cost of the mixture is $2.4\times55$. So the equation is $3.3x+2.2(55 - x)=2.4\times55$.

Step3: Expand and simplify the equation

Expand $2.2(55 - x)$ to get $121-2.2x$. The equation becomes $3.3x + 121-2.2x=132$. Combine like - terms: $(3.3x-2.2x)+121 = 132$, which simplifies to $1.1x+121 = 132$.

Step4: Solve for $x$

Subtract 121 from both sides: $1.1x=132 - 121=11$. Then divide both sides by 1.1: $x=\frac{11}{1.1}=10$.

Step5: Find the amount of pine wood chips

The amount of pine wood chips is $55 - x=55 - 10 = 45$.

Answer:

Oak chips: 10 lb
Pine chips: 45 lb