Let's solve the problem step by step:

Information Given:

1. Ratio of money split: Zoe : Maria : Dima = $2 : 5 : 8$.
2. Let the total amount of money divided be $x$.
3. The amounts received by Zoe, Maria, and Dima are proportional to the ratio, so:
   • Zoe receives $\frac{2}{15}x$,
   • Maria receives $\frac{5}{15}x = \frac{1}{3}x$,
   • Dima receives $\frac{8}{15}x$.
4. The total of Maria's and Dima's money is given as $26 less than the total amount divided, i.e.: $\text{Maria's money + Dima's money} = x - 26$

Step 1: Express Maria's and Dima's money

Maria's share: $\text{Maria's money} = \frac{5}{15}x = \frac{1}{3}x$ Dima's share: $\text{Dima's money} = \frac{8}{15}x$ The sum of Maria's and Dima's money is: $\text{Maria + Dima} = \frac{1}{3}x + \frac{8}{15}x$

Step 2: Combine terms with a common denominator

The least common denominator of $3$ and $15$ is $15$. Rewrite the terms: $\frac{1}{3}x = \frac{5}{15}x$ So: $\frac{1}{3}x + \frac{8}{15}x = \frac{5}{15}x + \frac{8}{15}x = \frac{13}{15}x$

Step 3: Set up the equation

It is given that: $\frac{13}{15}x = x - 26$

Step 4: Solve for $x$

Rearrange the equation: $x - \frac{13}{15}x = 26$ Factor out $x$: $\left( 1 - \frac{13}{15} \right)x = 26$ Simplify: $\frac{15}{15} - \frac{13}{15} = \frac{2}{15}$ So: $\frac{2}{15}x = 26$

Solve for $x$: $x = 26 \times \frac{15}{2}$ $x = 390$

Step 5: Find Maria's share

Maria's share is: $\text{Maria's money} = \frac{1}{3}x = \frac{1}{3}(390) = 130$

Final Answer:

Maria has $130.

Would you like a breakdown of any specific step?

Related Questions:

1. What is the total amount of money Dima received?
2. How much more money did Dima receive compared to Zoe?
3. If the total money was increased by 10%, how much would Maria get?
4. What percentage of the total money did Maria receive?
5. What is the difference in amounts received by Maria and Zoe?

Tip:

When solving ratio problems, always express amounts in terms of a single variable to simplify the calculations.