Answer:
The amount invested in the account paid 4% is $1150
The amount invested in the account paid 6% is $600
Explanation:
The rule of the simple interest is I = Prt, where
∵ Helene invested a total of $1,750 in two simple-interest bank accounts
∴ P1 + P2 = 1750 ⇒ (1)
∵ One account paid 4% annual interest
∴ r1 = 4% = 4/100 = 0.04
∵ The other paid 6% annual interest
∴ r2 = 6% = 6/100 = 0.06
∵ The total amount of interest she earned after 1 year was $82
∴ I1 + I2 = 82 ⇒ (2)
∵ t = 1
∵ I1 = P1 × (0.04) × 1
∴ I1 = 0.04 P1
∵ I2 = P2 × (0.06) × 1
∴ I2 = 0.06 P2
→ Substitute them in equation (2)
∴ 0.04 P1 + 0.06 P2 = 82 ⇒ (3)
Now we have a system of equations to solve it
→ Multiply equation (1) by -0.06 to make the coefficients of y equal in
values and different in signs to eliminate it
∵ -0.06(P1) + -0.06(P2) = -0.06(1750)
∴ -0.06 P1 + -0.06 P2 = -105 ⇒ (4)
→ Add equations (3) and (4)
∵ (0.04 P1 + -0.06 P2) + (0.06 P2 + -0.06 P2) = (82 + -105)
∴ -0.02 P1 + 0 P2 = -23
∴ -0.02 P1 = -23
→ Divide both sides by -0.02
∴ P1 = 1150
→ Substitute the value of P1 in equation (1) to find P2
∵ 1150 + P2 = 1750
→ Subtract both sides by 1150 to find P2
∴ P2 = 600
∴ The amount invested in the account paid 4% is $1150
∴ The amount invested in the account paid 6% is $600