Question
The expression 9.00x+4.50y represents the total amount of money Harriet earns at her two jobs, where x represents the number of hours worked at job X and y represents the number of hours worked at job Y. Which shows an equivalent expression to the given expression and correctly describes the situation?
4.50(2x+y), which shows that Harriet earns twice as much per hour at job X than at job Y
.
4.50(2x+y) which shows that Harriet earns 4.50 times as much per hour at job X than at job Y.
13.50xy, which shows that Harriet earns $13.50 each hour she works.
13.50xy, which shows that Harriet earns $13.50 every two hours she works.
closest answer
4.50(2x+y), which shows that Harriet earns twice as much per hour at job X than at job Y
.
4.50(2x+y) which shows that Harriet earns 4.50 times as much per hour at job X than at job Y.
13.50xy, which shows that Harriet earns $13.50 each hour she works.
13.50xy, which shows that Harriet earns $13.50 every two hours she works.
closest answer
Answers
GPT-4o mini
To analyze the expression \(9.00x + 4.50y\):
1. **\(x\)** represents hours worked at job X, where Harriet earns $9.00 per hour.
2. **\(y\)** represents hours worked at job Y, where Harriet earns $4.50 per hour.
We can factor out the common factor from the expression:
\[
9.00x + 4.50y = 4.50(2x + y)
\]
This indicates that she earns $4.50 per hour from job Y and $9.00 per hour from job X, which is indeed twice as much as what she earns at job Y.
Now, examining the answer choices:
1. **\(4.50(2x+y)\)**, which shows that Harriet earns twice as much per hour at job X than at job Y **(this is true)**.
2. **\(4.50(2x+y)\)** which shows that Harriet earns $4.50 times as much per hour at job X than at job Y **(this is incorrect)**.
3. **\(13.50xy\)**, which shows that Harriet earns $13.50 each hour she works **(this is incorrect)**.
4. **\(13.50xy\)**, which shows that Harriet earns $13.50 every two hours she works **(this is incorrect)**.
The closest answer that correctly describes the situation is:
**\(4.50(2x+y)\)**, which shows that Harriet earns twice as much per hour at job X than at job Y.
1. **\(x\)** represents hours worked at job X, where Harriet earns $9.00 per hour.
2. **\(y\)** represents hours worked at job Y, where Harriet earns $4.50 per hour.
We can factor out the common factor from the expression:
\[
9.00x + 4.50y = 4.50(2x + y)
\]
This indicates that she earns $4.50 per hour from job Y and $9.00 per hour from job X, which is indeed twice as much as what she earns at job Y.
Now, examining the answer choices:
1. **\(4.50(2x+y)\)**, which shows that Harriet earns twice as much per hour at job X than at job Y **(this is true)**.
2. **\(4.50(2x+y)\)** which shows that Harriet earns $4.50 times as much per hour at job X than at job Y **(this is incorrect)**.
3. **\(13.50xy\)**, which shows that Harriet earns $13.50 each hour she works **(this is incorrect)**.
4. **\(13.50xy\)**, which shows that Harriet earns $13.50 every two hours she works **(this is incorrect)**.
The closest answer that correctly describes the situation is:
**\(4.50(2x+y)\)**, which shows that Harriet earns twice as much per hour at job X than at job Y.