Manuel and ruben both have bank accounts. the system of equations models their balances after x weeks. y = 11.5x + 22 y = –13x + 218 their balances will be the same after weeks. their balances will be $

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

10.4 inches

step-by-step explanation:

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