Answer:
The amount invested in the account paid 4% is $1150
The amount invested in the account paid 6% is $600
Step-by-step explanation:
The rule of the simple interest is <em>I = Prt</em>, where
- <em>P</em> is the amount invested
- <em>r</em> is the rate in decimal
∵ Helene invested a total of $1,750 in two simple-interest bank accounts
∴ <em>P</em>1 + <em>P</em>2 = 1750 ⇒ (1)
∵ One account paid 4% annual interest
∴ <em>r</em>1 = 4% = 4/100 = 0.04
∵ The other paid 6% annual interest
∴ <em>r</em>2 = 6% = 6/100 = 0.06
∵ The total amount of interest she earned after 1 year was $82
∴ <em>I</em>1 +<em> I</em>2 = 82 ⇒ (2)
∵ t = 1
∵ <em>I</em>1 = P1 × (0.04) × 1
∴<em> </em><em>I</em>1 = 0.04 <em>P</em>1
∵<em> I</em>2 = P2 × (0.06) × 1
∴<em> </em><em>I</em>2 = 0.06<em> P</em>2
→ Substitute them in equation (2)
∴ 0.04 <em>P</em>1 + 0.06 <em>P</em>2 = 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(<em>P</em>1) + -0.06(<em>P</em>2) = -0.06(1750)
∴ -0.06 <em>P</em>1 + -0.06 <em>P</em>2 = -105 ⇒ (4)
→ Add equations (3) and (4)
∵ (0.04 <em>P</em>1 + -0.06 <em>P</em>2) + (0.06 <em>P</em>2 + -0.06 <em>P</em>2) = (82 + -105)
∴ -0.02 <em>P</em>1 + 0 <em>P</em>2 = -23
∴ -0.02 <em>P</em>1 = -23
→ Divide both sides by -0.02
∴ <em>P</em>1 = 1150
→ Substitute the value of <em>P</em>1 in equation (1) to find P2
∵ 1150 + <em>P</em>2 = 1750
→ Subtract both sides by 1150 to find P2
∴ <em>P</em>2 = 600
∴ The amount invested in the account paid 4% is $1150
∴ The amount invested in the account paid 6% is $600