Answer:
You should invest $820 in account A and $940 in account B
Step-by-step explanation:
* Lets use the system of linear equations to solve the problem
- Simple Interest Equation I = Prt , Where:
# P = Invested Amount
# I = Interest Amount
# r = Rate of Interest per year in decimal; r = R/100
# t = Time Period involved in months or years
* Lets solve the problem
- The total money invested is $1760
- Account A pays 7% annual interest
- Account B pays 4% annual interest
- Let A represent the amount of money invested in the account A
- Let B represent the amount of money invested in the account B
- You would like to earn $ 95 at the end of one year
∴ The interest from both accounts at the end of one year is $95
- Lets write the equations
# Account A :
∵ Account A has $A invested
∴ P = $A
∵ Account A pays 7% annual interest
∴ r = 7/100 = 0.07
∵ t = 1 year
∵ I = Prt
∴ I = A(0.07)(1) = 0.07A
# Account B :
∵ Account B has $B invested
∴ P = $B
∵ Account A pays 4% annual interest
∴ r = 4/100 = 0.04
∵ t = 1 year
∵ I = Prt
∴ I = B(0.04)(1) = 0.04B
- The total amount of interest from both accounts at the end of one
year is $95
∴ I from A + I from B = 95
∴ 0.07A + 0.04B = 95 ⇒ multiply both sides by 100
∴ 7A + 4B = 9500 ⇒ (1)
- The total money to invest in both accounts is $1760
∵ Account A has $A invested
∵ Account B has $B invested
∴ A + B = 1760 ⇒ (2)
* Lets solve the system of equations to find the amount of money
invested in each account
- Multiply equation (2) by -4 to eliminate B
∵ A + B = 1760 ⇒ × -4
∴ -4A - 4B = -7040 ⇒ (3)
- Add equation (1) and (3)
∵ 7A + 4B = 9500 ⇒ (1)
∵ -4A - 4B = -7040 ⇒ (3)
∴ 7A - 4A = 9500 - 7040
∴ 3A = 2460 ⇒ divide both side by 3
∴ A = 820
- Substitute the value of A in equation (1) or (2)
∵ A + B = 1760 ⇒ (2)
∴ 820 + B = 1760 ⇒ subtract 820 from both sides
∴ B = 940
- From all above
* You should invest $820 in account A and $940 in account B
.