An actor invests some money at 8% simple interest, and $21 comma 000 more than four times the amount at 10% simple interest. The total annual interest earned from the investment is $49 comma 140. How much did he invest at each amount? Use the six-step method.

First investment = $98000

Second = $413,000

Step-by-step explanation:

Given the following :

Investment 1:

Let first investment = f

Rate = 8% = 0.08

Investment 2:

$21,000 more than 4 times of investment 1:

4f + 21000

Rate = 10% = 0.1

Total annual interest earned from both :

$49,140

Interest on investment 1 + interest on investment 2 = $49,140

To solve:

Simple Interest = principal * rate * time

Time = 1 year

Total interest = (f * 0.08 * 1) + ((4f + 21000) * 0.1 * 1)

49140 = 0.08f + 0.4f + 2100

0.48f = 47040

f = 47040 / 0.48

f = 98000 = first investment

Second investment :

4f + 21000

= 4(98000) + 21000

= $413,000

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18