Question

Phyllis invested $12,000, part at 14% annual interest and the remainder at 10%. Last year she earned $1632 in interest. How much money did she invest at each rate?

Answer 1

Amount invested at 14% is $10,800
Amount invested at 10% is $1,200

Explanation:

Let x be the amount invested at 14% interest

Let y be the amount invested at 10% interest

Total investment :
x + y = 12000 [1]

Interest earned on x at 14% interest = 0.14x (14% = 14/100 in decimal)
Interest earned on y at 10% interest = 0.10y (10% = 10/100 in decimal)

Total Interest earned:
0.14x + 0.10y = 1632 [2]

Eliminate the y terms in the equation and solve for x; Then substituting value of x in any one equation solve for y

• Multiply [1] by 0.10
  01.0(x + y) = 0.10(12000)
  0.10x + 0.10y = 1200 [3]
  
• Subtract [3] from [2]
  
  0.14x + 0.10y = 1632
  -
  0.10x + 0.10y = 1200
  ----------------------------
  0.04x = 432
  -----------------------------
  
• Divide both sides by 0.04 to get the value of x
  0.04x/0.04 = 432/0.04
  x = 10,800
  
• Substitute this value of x in [1]:
  10800 + y = 12000
  y = 12000 - 10800
  y = 1200
  
• ANSWER
  Amount invested at 14% is $10,800
  Amount invested at 10% is $1,200