24 March, 17:18

# jose invests money in two simple interests account. he invests twice as much in an account paying 13% as he does in an account paying 5%. if he earns \$93.00 in interest in one year from both accounts combined how much did he invest altogether

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1. 24 March, 18:07
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He invested altogether \$900

Step-by-step explanation:

* Lets explain how to solve the problem

- Jose invests money in two simple interests account

- He invests twice as much in an account paying 13% as he does in

an account paying 5%

- That means the amount he invested in the account paying 13% is

twice the amount he invested in the account paying 5%

- He earns \$93.00 in interest in one year from both accounts combined

- We need to find how much he invested in each account

- Assume that he invested \$x in the account paying 5%

∵ He invested twice as much in an account paying 13% as he does in

an account paying 5%

∴ He invested \$2x in the account paying 13%

- The simple interest I = PRT, where P is the money invested, R is the

rate of interest in decimal and t is the time of investment

# Account paying 13%

∵ P = 2x, R = 13/100 = 0.13, T = 1

∴ I = 2x (0.13) (1)

∴ I = 0.26 x ⇒ (1)

# Account paying 5%

∵ P = x, R = 5/100 = 0.05, T = 1

∴ I = x (0.05) (1)

∴ I = 0.05 x ⇒ (2)

∵ He earns \$93.00 in interest in one year from both accounts

- Add (1) and (2) and equate the sum by 93.00

∴ 0.26 x + 0.05 x = 93.00

- Add like terms in the left hand side

∴ 0.31 x = 93.00

- Divide both sides by 0.31

∴ x = 300

∴ 2x = 2 (300)

∴ 2x = 600

∵ x represents the amount of money invested in the account paying 5%

∴ The amount of money invested in the account of 5% is \$300

∴ The amount of money invested in the account of 13% is \$600

- The total amount of money he invested is the sum of the money

he invested in each account [\$300 + \$600 = \$900]

∴ He invested altogether \$900