C. 16 Solve linear equations with variables on both sides: word problems H9G Joy bought some granola from the bulk bins at the grocery store. Emilio bought one-third as much granola as Joy, but he also spent \( \$ 4.41 \) on milk and \( \$ 6.17 \) on fresh berries. Joy and Emilio ended up spending the same amount of money. How much did Joy spend on granola?

Let's denote the amount of granola Joy bought as \( x \) pounds. According to the problem, Emilio bought one-third as much granola as Joy, which means he bought \( \frac{1}{3}x \) pounds of granola. The total amount of money Joy spent is the cost of the granola, which is \( x \) dollars. The total amount of money Emilio spent is the cost of the granola plus the cost of milk and fresh berries, which is \( \frac{1}{3}x + 4.41 + 6.17 \) dollars. Since Joy and Emilio ended up spending the same amount of money, we can set up the equation: \[ x = \frac{1}{3}x + 4.41 + 6.17 \] Now, we can solve this equation to find the value of \( x \), which represents the amount of money Joy spent on granola. Solve the equation by following steps: - step0: Solve for \(x\): \(x=\frac{1}{3}x+4.41+6.17\) - step1: Add the numbers: \(x=\frac{1}{3}x+10.58\) - step2: Move the variable to the left side: \(x-\frac{1}{3}x=10.58\) - step3: Subtract the terms: \(\frac{2}{3}x=10.58\) - step4: Multiply by the reciprocal: \(\frac{2}{3}x\times \frac{3}{2}=10.58\times \frac{3}{2}\) - step5: Multiply: \(x=\frac{1587}{100}\) The solution to the equation is \( x = 15.87 \) pounds. Therefore, Joy spent $15.87 on granola.