Question

Susanna has $65 and is continuing to save $10 per week. Her friend, Jasmine, has $30 and is saving $15 per week. Which inequality shows when Jasmine will have more money than Susanna?

a) 10x + 65 > 15x + 30
b) 10x + 30 > 15x + 65
c) 15x + 30 > 10x + 65
d) 15x + 65 > 10x + 30

Answer 1

The inequality that shows when Jasmine will have more money than Susanna is c) 15x + 30 > 10x + 65. It represents the situation where Jasmine's weekly savings of $15 surpass Susanna's savings of $10 over time starting from their initial amounts of $30 and $65 respectively.

Step-by-step explanation:

The correct inequality to show when Jasmine will have more money than Susanna is c) 15x + 30 > 10x + 65. This inequality represents the situation where Jasmine, starting with $30 and saving $15 per week, will have more money than Susanna, who starts with $65 and saves $10 per week.

We can demonstrate this with a step-by-step approach:

1. Let x represent the number of weeks.
2. Susanna's amount of money as a function of time can be given by the expression 10x + 65, where $65 is her starting amount and she adds $10 for each week.
3. Similarly, Jasmine's amount can be represented by the expression 15x + 30, where she starts with $30 and adds $15 each week.
4. To find out when Jasmine will have more money than Susanna, we want Jasmine's total to be greater than Susanna's, which translates to the inequality 15x + 30 > 10x + 65.