Chris has $400 in his bank account and he deposits$5 per week thereafter into hisaccount. His brother Ben has $582 in his accountand withdraws $8 per week fromhis account. Assuming this pattern continues, writeand solve an equation to determine how manyweeks it will take for them to have the sameamounts in their bank accounts.
Mathematics · Middle School · Tue Nov 03 2020
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Given the statement:
Chris has $400 in his bank account and he deposits$5 per week thereafter into hisaccount. His brother Ben has $582 in his accountand withdraws $8 per week fromhis account.
Determine the pattern and how many weeks would it take for them to have the same amount of in their bank accounts.
Representation:
Let x = number of weeks
Chris: 400 + 5x
Ben: 582 + 8x
Solution:
In order to determine the answer for the given problem,. we must equate the solution in one representation since we are asked for the number of weeks that there amount will be the same.
400 + 5x = 582 + 8x
Transpose 400 and 8x on the opposite side of the equation, note that when transposing a number, the sign changes.
582 - 400 = -8x + 5x
182 = -3x
Noticed that if we divide both sides by -3 the answer will be negative, and we cannot have a negative answer. This means that their money cannot be equal after how many weeks since Ben already have a greater amount of money compared to Chris, and Ben is also depositing a greater amount compared to Ben. Therefore their money will never be equal.