Question
Krystal and Desmond have both been hired at their local grocery store to bag groceries and stock shelves. They are looking to keep track of the amount of money they are saving up. Look at how much each of them has saved and how much money they are making per hour.
Wage: $10.30 per hour Money already saved: $15.50
Wage: $10.30 per hour Money already saved: $12
Put in "True" for the statements that are true and "False"" for any statements that are not true.
Krystal and Dave have the same rate of change
Krystal has more money saved than Desmond if they work the same number of hours
Desmond needs to work 3 1/2 more hours than Krystal to have the same amount of money
If you graph both Krystal's and Desmond's savings, both graphs would show a positive, linear scenario
Wage: $10.30 per hour Money already saved: $15.50
Wage: $10.30 per hour Money already saved: $12
Put in "True" for the statements that are true and "False"" for any statements that are not true.
Krystal and Dave have the same rate of change
Krystal has more money saved than Desmond if they work the same number of hours
Desmond needs to work 3 1/2 more hours than Krystal to have the same amount of money
If you graph both Krystal's and Desmond's savings, both graphs would show a positive, linear scenario
Answers
GPT-4o mini
Let's evaluate each statement one by one based on the provided information.
1. **Krystal and Desmond have the same rate of change.**
- **True.** Both Krystal and Desmond have the same wage of $10.30 per hour, which means they have the same rate of change regarding how much money they save per hour worked.
2. **Krystal has more money saved than Desmond if they work the same number of hours.**
- **True.** Krystal already has saved $15.50, which is greater than Desmond's $12. Therefore, if they work the same number of hours, Krystal will still have more money saved.
3. **Desmond needs to work 3 1/2 more hours than Krystal to have the same amount of money.**
- **False.** Let's calculate how much more Desmond needs to save:
- The difference in their savings is $15.50 - $12 = $3.50.
- To find out how many hours Desmond needs to work to catch up, we can use his hourly wage:
\[
\text{Hours needed} = \frac{\text{Difference}}{\text{Wage}} = \frac{3.50}{10.30} \approx 0.34 \text{ hours} \, (\text{or about 20.4 minutes}),
\]
- Not 3.5 hours, so this statement is false.
4. **If you graph both Krystal's and Desmond's savings, both graphs would show a positive, linear scenario.**
- **True.** Since they both have a fixed hourly wage, their savings can be represented as linear functions of time, indicating a positive slope.
Based on these evaluations, the answers are:
1. True
2. True
3. False
4. True
1. **Krystal and Desmond have the same rate of change.**
- **True.** Both Krystal and Desmond have the same wage of $10.30 per hour, which means they have the same rate of change regarding how much money they save per hour worked.
2. **Krystal has more money saved than Desmond if they work the same number of hours.**
- **True.** Krystal already has saved $15.50, which is greater than Desmond's $12. Therefore, if they work the same number of hours, Krystal will still have more money saved.
3. **Desmond needs to work 3 1/2 more hours than Krystal to have the same amount of money.**
- **False.** Let's calculate how much more Desmond needs to save:
- The difference in their savings is $15.50 - $12 = $3.50.
- To find out how many hours Desmond needs to work to catch up, we can use his hourly wage:
\[
\text{Hours needed} = \frac{\text{Difference}}{\text{Wage}} = \frac{3.50}{10.30} \approx 0.34 \text{ hours} \, (\text{or about 20.4 minutes}),
\]
- Not 3.5 hours, so this statement is false.
4. **If you graph both Krystal's and Desmond's savings, both graphs would show a positive, linear scenario.**
- **True.** Since they both have a fixed hourly wage, their savings can be represented as linear functions of time, indicating a positive slope.
Based on these evaluations, the answers are:
1. True
2. True
3. False
4. True