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Sagot :
To find the correct expression representing the total amount of money Eric saves for working [tex]\(s\)[/tex] hours making sandwiches and [tex]\(d\)[/tex] hours delivering orders, let's carefully analyze each option given.
### Step-by-Step Analysis:
1. Determine Eric's Hourly Rates:
- For making sandwiches, Eric saves [tex]$10 per hour. Thus, if he works \(s\) hours making sandwiches, the total amount saved from this task is \(10s\) dollars. - For delivering orders, Eric saves $[/tex]14 per hour. If he works [tex]\(d\)[/tex] hours delivering orders, the total amount saved from this task is [tex]\(14d\)[/tex] dollars.
2. Combine the Two Tasks:
- To find the total amount of money Eric saves, we combine the savings from both tasks. This means we simply add the two amounts together: [tex]\(10s + 14d\)[/tex].
### Evaluating the Expressions:
- Option 1: [tex]\(10s + 14d\)[/tex]
This expression directly represents the total savings from both tasks:
[tex]\[ 10s + 14d \][/tex]
- Option 2: [tex]\(\frac{1}{2} \cdot 10s + 14d\)[/tex]
This expression modifies only the savings from making sandwiches by multiplying it by [tex]\( \frac{1}{2} \)[/tex], which is not what we are looking for:
[tex]\[ \frac{1}{2}(10s) + 14d = 5s + 14d \][/tex]
- Option 3: [tex]\(10s + 14d \div \frac{1}{2}\)[/tex]
This expression suggests dividing the entire savings from delivering orders by [tex]\( \frac{1}{2} \)[/tex], which is also incorrect:
[tex]\[ 10s + \frac{14d}{\frac{1}{2}} = 10s + 28d \][/tex]
- Option 4: [tex]\(\frac{1}{2}(10s + 14d)\)[/tex]
This expression divides the total savings from both tasks by [tex]\( \frac{1}{2} \)[/tex], which changes the total and is incorrect:
[tex]\[ \frac{1}{2}(10s + 14d) = 5s + 7d \][/tex]
### Conclusion:
The correct expression that represents the total amount of money Eric saves for working [tex]\(s\)[/tex] hours making sandwiches and [tex]\(d\)[/tex] hours delivering orders is:
[tex]\[ 10s + 14d \][/tex]
This option directly sums the savings from both tasks accurately.
### Step-by-Step Analysis:
1. Determine Eric's Hourly Rates:
- For making sandwiches, Eric saves [tex]$10 per hour. Thus, if he works \(s\) hours making sandwiches, the total amount saved from this task is \(10s\) dollars. - For delivering orders, Eric saves $[/tex]14 per hour. If he works [tex]\(d\)[/tex] hours delivering orders, the total amount saved from this task is [tex]\(14d\)[/tex] dollars.
2. Combine the Two Tasks:
- To find the total amount of money Eric saves, we combine the savings from both tasks. This means we simply add the two amounts together: [tex]\(10s + 14d\)[/tex].
### Evaluating the Expressions:
- Option 1: [tex]\(10s + 14d\)[/tex]
This expression directly represents the total savings from both tasks:
[tex]\[ 10s + 14d \][/tex]
- Option 2: [tex]\(\frac{1}{2} \cdot 10s + 14d\)[/tex]
This expression modifies only the savings from making sandwiches by multiplying it by [tex]\( \frac{1}{2} \)[/tex], which is not what we are looking for:
[tex]\[ \frac{1}{2}(10s) + 14d = 5s + 14d \][/tex]
- Option 3: [tex]\(10s + 14d \div \frac{1}{2}\)[/tex]
This expression suggests dividing the entire savings from delivering orders by [tex]\( \frac{1}{2} \)[/tex], which is also incorrect:
[tex]\[ 10s + \frac{14d}{\frac{1}{2}} = 10s + 28d \][/tex]
- Option 4: [tex]\(\frac{1}{2}(10s + 14d)\)[/tex]
This expression divides the total savings from both tasks by [tex]\( \frac{1}{2} \)[/tex], which changes the total and is incorrect:
[tex]\[ \frac{1}{2}(10s + 14d) = 5s + 7d \][/tex]
### Conclusion:
The correct expression that represents the total amount of money Eric saves for working [tex]\(s\)[/tex] hours making sandwiches and [tex]\(d\)[/tex] hours delivering orders is:
[tex]\[ 10s + 14d \][/tex]
This option directly sums the savings from both tasks accurately.
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