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.

Question

How much did Joy spend on granola?

Answer 1

Let \( x \) be the amount of money Joy spent on granola.

Emilio bought one-third as much granola as Joy, so the amount he spent on granola is \( \frac{x}{3} \).

Emilio also spent an additional $4.41 on milk and $6.17 on fresh berries, so the total amount Emilio spent is:

\[ \frac{x}{3} + 4.41 + 6.17 \]

We know that Joy and Emilio ended up spending the same amount of money. Therefore, we can set up the equation:

\[ x = \frac{x}{3} + 4.41 + 6.17 \]

First, combine the constants on the right-hand side:

\[ 4.41 + 6.17 = 10.58 \]

Now the equation simplifies to:

\[ x = \frac{x}{3} + 10.58 \]

To eliminate the fraction, multiply the entire equation by 3:

\[ 3x = x + 31.74 \]

Next, isolate \( x \) by subtracting \( x \) from both sides:

\[ 3x - x = 31.74 \] \[ 2x = 31.74 \]

Now, divide both sides by 2:

\[ x = \frac{31.74}{2} = 15.87 \]

Thus, Joy spent \( \boxed{15.87} \) dollars on granola.