21. metalworking how many 2.34 - in. spacer blocks can be cut from a 2 - in. by 2 - in. square bar 48 in…
21. metalworking how many 2.34 - in. spacer blocks can be cut from a 2 - in. by 2 - in. square bar 48 in. long? allow $\frac{1}{4}$ in. waste for each saw cut.
Answer
Explanation:
Step1: Consider waste per cut
Let the number of spacer blocks be $n$. The number of cuts is $n - 1$. The total waste from cuts is $\frac{1}{4}(n - 1)$ inches.
Step2: Set up length - related equation
The length used for the spacer blocks plus the total waste equals the length of the bar. Each spacer block is 2.34 inches long. So we have the equation $2.34n+\frac{1}{4}(n - 1)=48$. Expand the equation: $2.34n+\frac{1}{4}n-\frac{1}{4}=48$. Combine like - terms: $(2.34 + 0.25)n-\frac{1}{4}=48$, which is $2.59n-\frac{1}{4}=48$. Add $\frac{1}{4}$ (or 0.25) to both sides: $2.59n=48 + 0.25=48.25$.
Step3: Solve for n
Divide both sides by 2.59: $n=\frac{48.25}{2.59}\approx18.63$. Since we can't have a fraction of a block, we take the whole number part.
Answer:
18