Buying 5 apples and a $4 mango is the same as buying 7 apples and a mandarin which costs $2 (use a as the price for apples) Write an equation and find the cost of the apples

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.

Buying 5 apples and a $4 mango is the same as buying 7 apples and a mandarin which costs $2 (use a as the price for apples). Write an equation and find the cost of the apples.

Learn how to solve a linear equation involving the cost of apples, mangoes, and mandarins. This problem demonstrates algebraic concepts like setting up and solving linear equations with variables and constants. Suitable for students in Grades 6-8.

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