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

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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.

Answer 1

To analyze the expression \(9.00x + 4.50y\) more closely, we see that:

• Harriet earns $9.00 per hour at job X (for \(x\) hours).
• Harriet earns $4.50 per hour at job Y (for \(y\) hours).

Now, we can evaluate the given options for equivalency and for their correctness in describing the situation.

1. Option 1: \(4.50(2x + y)\)

   • This implies that Harriet earns $4.50 per hour at job X, which is incorrect; she earns $9.00 at job X. Thus, this option is incorrect.

2. Option 2: \(4.50(2x + y)\)

   • Similar to option 1, this implies Harriet earns $4.50 per hour at job X, which is incorrect. So, this option is also incorrect.

3. Option 3: \(13.50xy\)

   • This expression does not reflect her earnings from the two jobs correctly. It implies that she earns $13.50 per hour altogether, but doesn't accurately represent the individual rates and hours worked, so this is incorrect.

4. Option 4: \(13.50xy\)

   • Like option 3, this doesn't represent the earnings correctly and implies a combined earnings structure that doesn’t match the hourly rates. Thus, this is incorrect as well.

After examining each option, none of the provided expressions accurately represents the original expression \(9.00x + 4.50y\) and describes Harriet's earnings correctly.

However, if we were to express \(9.00x + 4.50y\) in a form that relates to the actual hourly rates, a correct equivalent would look like \(9.00x + 4.50y\) as it stands, without factoring incorrectly or misrepresenting the jobs.