Ellie and Tanya each have bank accounts.Ellie has $500 and Tanya has $200.Ellie withdraws $15 each weekend while Tanya deposits $12.At the end of 13 weeks what is the difference in their bank accounts?Solve this algebraically.Can you find a week when there is only a $3 difference?

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To solve this problem algebraically, we can represent the amount of money in Ellie's bank account after each week using the equation: E = 500 - 15w, where w represents the number of weeks.

Similarly, we can represent the amount of money in Tanya's bank account after each week using the equation: T = 200 + 12w.

To find the difference in their bank accounts at the end of 13 weeks, we need to find the value of E - T when w = 13. Substitute w = 13 into the equations:

E = 500 - 15 * 13 = 500 - 195 = 305
T = 200 + 12 * 13 = 200 + 156 = 356

So, the difference in their bank accounts after 13 weeks is 305 - 356 = -51. The negative sign indicates that Ellie's account has less money than Tanya's account.

To determine if there is a week when there is only a $3 difference, we set E - T = 3 and solve for w:

500 - 15w - (200 + 12w) = 3
500 - 200 - 3 = 15w + 12w
297 = 27w
w = 11

So, there is a week when there is only a $3 difference between their bank accounts, and that week is the 11th week.