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?

Question

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

Answer 1

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.