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Andrews [41]
3 years ago
9

jose invests money in two simple interests account. he invests twice as much in an account paying 13% as he does in an account p

aying 5%. if he earns $93.00 in interest in one year from both accounts combined how much did he invest altogether​
Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
7 0

Answer:

He invested altogether $900

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- 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 <em>I = PRT</em>, where P is the money invested, R is the

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

# <u><em>Account paying 13%</em></u>

∵ P = 2x , R = 13/100 = 0.13 , T = 1

∴ I = 2x(0.13)(1)

∴ I = 0.26 x ⇒ (1)

# <u><em>Account paying 5%</em></u>

∵ 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%

∴ <em>The amount of money invested in the account of 5% is $300</em>

∴ <em>The amount of money invested in the account of 13% is $600</em>

- 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

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