Someone invested some money at 8% and $300 more than
twice this amount at 12%. Her total annual income from
the two investments is $548. How much is invested at
each rate?
32

Respuesta :

Answer:

$1600 at 8% and 3500 at 12%

Step-by-step explanation:

The rule of the interest is I = PRT, where

  • P is the amount of investment
  • R is the rate in decimal
  • T is the time

Assume that the amount of money is $x

P = x

∵ The rate is 8%

R = 8/100 = 0.08

∵ She has an annual income

T = 1

→ Substitute them in the rule to find the interest amount

∴ I = x × 0.08 × 1

I = 0.08x

∵ She invested $300 more than twice the previous amount

P = 2x + 300

∵ The rate is 12%

R = 12/100 = 0.12

T = 1

→ Substitute them in the rule to find the other interest amount

∴ I = (2x + 300) × 0.12 × 1

I = 0.24x + 36

∵ Her total annual income from both investments is $548

→ Add the two amount of interest and equate their sum by 548

0.08x + 0.24x + 36 = 548

→ Add the like terms in the left side

∴ 0.32x + 36 = 548

→ Subtract 36 from both sides

∴ 0.32x + 36 - 36 = 548 - 36

∴ 0.32x = 512

→ Divide both sides by 0.32

x = 1600

She invested $1600 at 8%

→ Substitute x by 1600 in the expression of the other amount to find it

∵ 2x + 300 = 2(1600) + 300 = 3500

She invested $3500 at 12%