Let's break down the problem step by step.

• The price of one apple is denoted by $a$.
• The cost of buying 5 apples is $5a$.
• The cost of a mango is $4.
• The cost of buying 7 apples is $7a$.
• The cost of a mandarin is $2.

We are told that buying 5 apples and a $4 mango is the same as buying 7 apples and a $2 mandarin. So, we can set up the following equation:

$5a + 4 = 7a + 2$

Solving for $a$:

1. Subtract $5a$ from both sides to get the apples on one side: $4 = 2a + 2$

2. Subtract 2 from both sides: $2 = 2a$

3. Divide by 2: $a = 1$

So, the price of one apple is $1.

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

Here are 5 related questions to explore further:

1. What if the price of the mango was $5 instead of $4?
2. How would the equation change if the mandarin cost $3?
3. If you bought 10 apples and a mango, what would be the total cost?
4. How would the equation look if you bought twice as many apples?
5. How would the problem change if you got a 10% discount on the apples?

Tip: When solving equations, always isolate the variable step by step by using inverse operations like addition, subtraction, multiplication, or division.