14. make sense and persevere clint prepares and sells trail mixes at his store. this week, he uses…
14. make sense and persevere clint prepares and sells trail mixes at his store. this week, he uses $\frac{3}{8}$ of his supply of raisins to make regular trail mix and $\frac{1}{4}$ of his supply to make spicy trail mix. if clint uses 20 pounds of raisins this week, how many pounds of raisins did he have at the beginning of the week?
Answer
Explanation:
Step1: Find the total fraction of raisins used
First, find a common - denominator for $\frac{3}{8}$ and $\frac{1}{4}$. The common denominator of 8 and 4 is 8. Since $\frac{1}{4}=\frac{2}{8}$, the total fraction of raisins used is $\frac{3}{8}+\frac{2}{8}=\frac{3 + 2}{8}=\frac{5}{8}$.
Step2: Set up an equation to find the original amount
Let $x$ be the amount of raisins at the beginning of the week. We know that $\frac{5}{8}x = 20$.
Step3: Solve the equation for $x$
To solve for $x$, we multiply both sides of the equation $\frac{5}{8}x = 20$ by $\frac{8}{5}$. So $x=20\times\frac{8}{5}=\frac{20\times8}{5}=32$.
Answer:
32