Answer:
$1600 at 8% and 3500 at 12%
Step-by-step explanation:
The rule of the interest is I = PRT, where
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%