$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
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( [tex]\frac{7}{100}[/tex] )(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)( [tex]\frac{6}{100}[/tex] )(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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