Let the amount of money Brian has be denoted as $B$. According to the problem, we are given the following relationship:

$\frac{2}{3} \times 2.40 + \frac{5}{7} \times B = \frac{3}{5} \times 11.25$

Step 1: Simplify each part

• First, calculate $\frac{2}{3} \times 2.40$: $\frac{2}{3} \times 2.40 = \frac{4.80}{3} = 1.60$

• Next, calculate $\frac{3}{5} \times 11.25$: $\frac{3}{5} \times 11.25 = \frac{33.75}{5} = 6.75$

Thus, the equation becomes: $1.60 + \frac{5}{7} \times B = 6.75$

Step 2: Isolate $B$

Subtract $1.60$ from both sides: $\frac{5}{7} \times B = 6.75 - 1.60$ $\frac{5}{7} \times B = 5.15$

Now, multiply both sides of the equation by $\frac{7}{5}$ to solve for $B$: $B = 5.15 \times \frac{7}{5}$ $B = \frac{5.15 \times 7}{5} = \frac{36.05}{5} = 7.21$

Final Answer:

Brian has $7.21.

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Would you like more details on the steps, or do you have any other questions?

Here are five related questions:

1. How do you solve a similar equation with different fractions?
2. What happens if the fractions are changed in the original problem?
3. How can you use algebra to represent financial word problems?
4. What other ways could you simplify fractional equations like this one?
5. How does the distributive property work with fractions in equations?

Tip: When working with fractions in word problems, always try to isolate the variable step by step. Simplifying both sides of the equation makes it easier to find the unknown.