Miko likes arranging fruit platters. In a fruit platter competition Miko joined, the ratio of apples to papayas the organiser prepared was 1: 5. If 92 papayas were added, the ratio of apples to papayas would be 1: 7. How many apples were there?

Let the number of apples be \( a \), and the number of papayas be \( p \).

We are given the following two pieces of information:

1. Initially, the ratio of apples to papayas is 1:5, which means:

\[
\frac{a}{p} = \frac{1}{5} \quad \text{or} \quad a = \frac{1}{5}p
\]

2. After 92 papayas are added, the new ratio of apples to papayas becomes 1:7, so:

\[
\frac{a}{p + 92} = \frac{1}{7} \quad \text{or} \quad a = \frac{1}{7}(p + 92)
\]

### Step 1: Express \( a \) in terms of \( p \)
From the first equation, we know that \( a = \frac{1}{5}p \).

From the second equation, we have \( a = \frac{1}{7}(p + 92) \).

Since both expressions represent \( a \), we can set them equal to each other:

\[
\frac{1}{5}p = \frac{1}{7}(p + 92)
\]

### Step 2: Solve for \( p \)
Multiply both sides by 35 to eliminate the denominators:

\[
7p = 5(p + 92)
\]

Expand the right side:

\[
7p = 5p + 460
\]

Subtract \( 5p \) from both sides:

\[
2p = 460
\]

Solve for \( p \):

\[
p = 230
\]

### Step 3: Find \( a \)
Now that we know \( p = 230 \), substitute this value into the first equation to find \( a \):

\[
a = \frac{1}{5} \times 230 = 46
\]

Thus, the number of apples is \( \boxed{46} \).

Would you like further clarification or details on the solution?

Here are 5 related questions to explore:

1. If 10 more papayas were added to the final scenario, what would the new ratio be?
2. How many papayas were there initially in the competition?
3. What if the initial ratio was 1:4 instead of 1:5, and the same number of papayas were added?
4. What is the percentage increase in the number of papayas after 92 were added?
5. How would the ratios change if 20 apples were added instead?

**Tip**: When solving ratio problems, it's helpful to express unknowns in terms of one variable and use systems of equations to simplify the solution.

Learn how to solve a fruit ratio problem where the initial ratio of apples to papayas is 1:5. When 92 papayas are added, the ratio changes to 1:7. This step-by-step solution helps you understand ratio concepts and algebraic equation solving, suitable for Grades 6-8.

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