Question

Which situation can be modeled by the inequality 8x + 25 > 2. 50x + 40?

Ted has $40 in his savings account. Every week, he deposits $2. 50. Jan has $8 in heraccount. Every week, she deposits $25. After how many weeks will Jan have more money savedthan Ted?

Answer 1

To determine after how many weeks Jan will have more money saved than Ted, solve the inequality 8x + 25 > 2.50x + 40 for x. Upon calculation, Jan will have more money saved than Ted after more than 2 weeks. Therefore, Jan will have more savings starting from the 3rd week.

Step-by-step explanation:

The situation described can be modeled by the inequality 8x + 25 > 2.50x + 40, where x represents the number of weeks. To find after how many weeks Jan will have more money saved than Ted, we solve for x like so:

8x + 25 > 2.50x + 40

To isolate the variable x on one side of the inequality, we start by subtracting 2.50x from both sides:

5.50x + 25 > 40

Next, we subtract 25 from both sides to further isolate the variable:

5.50x > 15

Finally, we divide both sides by 5.50 to solve for x:

x > 15 / 5.50

x > 2.7272...

Thus, we conclude that Jan will have more money saved than Ted after more than 2 weeks, but since we cannot have a fraction of a week, we round up to the nearest whole week, which is 3 weeks.