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Answer :
- Calculate the number of earbuds per case: $\frac{8}{4} = 2$.
- Multiply the earbuds per case by the number of cases: $2 \times 12 = 24$.
- Alternatively, solve the proportion: $\frac{8}{4} = \frac{x}{12}$, which gives $x = 24$.
- The total number of earbuds in 12 cases is $\boxed{24}$.
### Explanation
1. Understanding the Problem
We are given that 4 cases hold 8 earbuds. We need to find out how many earbuds are in 12 cases. The problem suggests multiplying 8 by 3 to find the answer. Let's verify this approach.
2. Finding Earbuds per Case
First, we can find the number of earbuds per case by dividing the total number of earbuds by the number of cases:$$\frac{8 \text{ earbuds}}{4 \text{ cases}} = 2 \text{ earbuds per case}$$.
3. Calculating Total Earbuds
Now, we can find the total number of earbuds in 12 cases by multiplying the number of earbuds per case by the number of cases:$$2 \frac{\text{earbuds}}{\text{case}} \times 12 \text{ cases} = 24 \text{ earbuds}$$.
4. Using Proportions
Alternatively, we can set up a proportion:$$\frac{8 \text{ earbuds}}{4 \text{ cases}} = \frac{x \text{ earbuds}}{12 \text{ cases}}$$.Cross-multiplying, we get:$$4x = 8 \times 12$$$$4x = 96$$$$x = \frac{96}{4}$$$$x = 24 \text{ earbuds}$$.
5. Final Answer
Since $8 \times 3 = 24$, the problem's suggestion to multiply 8 by 3 is correct. Therefore, there are 24 earbuds in 12 cases.
### Examples
Understanding proportional relationships is useful in many real-life situations. For example, if you know the price of one item, you can calculate the price of multiple items. Similarly, if you know how much time it takes to complete a task, you can estimate how much time it will take to complete multiple tasks. This type of problem helps in budgeting, planning, and making informed decisions.
- Multiply the earbuds per case by the number of cases: $2 \times 12 = 24$.
- Alternatively, solve the proportion: $\frac{8}{4} = \frac{x}{12}$, which gives $x = 24$.
- The total number of earbuds in 12 cases is $\boxed{24}$.
### Explanation
1. Understanding the Problem
We are given that 4 cases hold 8 earbuds. We need to find out how many earbuds are in 12 cases. The problem suggests multiplying 8 by 3 to find the answer. Let's verify this approach.
2. Finding Earbuds per Case
First, we can find the number of earbuds per case by dividing the total number of earbuds by the number of cases:$$\frac{8 \text{ earbuds}}{4 \text{ cases}} = 2 \text{ earbuds per case}$$.
3. Calculating Total Earbuds
Now, we can find the total number of earbuds in 12 cases by multiplying the number of earbuds per case by the number of cases:$$2 \frac{\text{earbuds}}{\text{case}} \times 12 \text{ cases} = 24 \text{ earbuds}$$.
4. Using Proportions
Alternatively, we can set up a proportion:$$\frac{8 \text{ earbuds}}{4 \text{ cases}} = \frac{x \text{ earbuds}}{12 \text{ cases}}$$.Cross-multiplying, we get:$$4x = 8 \times 12$$$$4x = 96$$$$x = \frac{96}{4}$$$$x = 24 \text{ earbuds}$$.
5. Final Answer
Since $8 \times 3 = 24$, the problem's suggestion to multiply 8 by 3 is correct. Therefore, there are 24 earbuds in 12 cases.
### Examples
Understanding proportional relationships is useful in many real-life situations. For example, if you know the price of one item, you can calculate the price of multiple items. Similarly, if you know how much time it takes to complete a task, you can estimate how much time it will take to complete multiple tasks. This type of problem helps in budgeting, planning, and making informed decisions.
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