Answer:
The equal balances will be $114 after 8 weeks
Step-by-step explanation:
* Lets study the information in the problem
- Manuel and Ruben both have bank accounts
- The system of equations models their balances y after x weeks
- Manuel balance is y = 11.5x + 22
- Ruben balance is y = -13x + 218
- After x weeks they will have same balances, means the values of y
will be equal at the same values of x
- The solve the problem we will equate the two equations to find x
and then substitute this x in on of the equation s to find the
balance y
- Lets do that
∵ Manuel balance is y = 11.5x + 22
∵ Ruben balance is y = -13x + 218
∵ After x weeks their balances will be equal
- Equate the equations
∴ 11.5x + 22 = -13x + 218
- add 13 x for both sides
∴ 11.5x + 13x + 22 = 218
∴ 24.5x + 22 = 218
- subtract 22 from both sides
∴ 24.5x = 218 - 22
∴ 24.5x = 196
- Divide both sides by 24.5
∴ x = 8
- Their balances will be equals after 8 weeks
- To find the balance substitute x by 8 in any equation
∵ y = 11.5x + 22
∵ x = 8
∴ y = 11.5(8) + 22
∴ y = 92 + 22 = 114
∴ The equal balances will be $114
* The equal balances will be $114 after 8 weeks
