Question

Sherry invested some money at 7% interest Sherry also invested $242 more than four times that amount at 6% how much is invested at each rate if Sherry receives $427.13 in interest after one year

Answer 1

$1331 is invested at 7% and $5566 is invested at 6%

Step-by-step explanation:

The formula of the simple interest is I = P r t, where

• P is the money invested
• r is the rate of interest in decimal
• t is the time of investment

Assume that Sherry invested $P in the first account

∵ Sherry invested $P in the first account at 7% interest for 1 year

∵ I = P r t

∴ The interest of the 1st account = P( $\frac{7}{100}$ )(1)

∴ The interest of the 1st account = 0.07 P

∵ Sherry also invested $242 more than four times that amount at

   6% for 1 year

- Multiply P by 4 and add 242 to the product

∴ Sherry invested in the 2nd account (4P + 242)

∵ I = P r t

∴ The interest of the 2nd account = (4P + 242)( $\frac{6}{100}$ )(1)

∴ The interest of the 2nd account = 0.06(4P + 242)

- Simplify it

∴ The interest of the 2nd account = 0.24 P + 14.52

∵ Sherry receives $427.13 in interest after one year

- Equate the 1st interest and the 2nd interest and equate the sum

  by 427.13

∴ 0.07 P + 0.24 P + 14.52 = 427.13

∴ 0.31 P + 14.52 = 427.13

- Subtract 14.52 from both sides

∴ 0.31 P = 412.61

- Divide both sides by 0.31

∴ P = 1331

∵ She invested (4P + 242) in the 2nd account

- Substitute P by 1331

∴ She invested in the 2nd account = 4(1331) + 242 = 5566

∴ She invested $1331 at 7% interest

∴ She invested $5566 at 6% interest

$1331 is invested at 7% and $5566 is invested at 6%

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