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Chapter 12: Q26. (page 745)

Ms. Brinkman invested \(30,000; part at 5%, and part at 8%. The total interest on the investment was \)2100 after one year. How much did she invest at 8%?

  1. \(10,000
  2. \)15,000
  3. \(20,000
  4. \)25,000

Short Answer

Expert verified

Investment at 8% is $20,000. Option C.

Step by step solution

01

Step 1. Write the formula for Simple interest.

Interest is given by:

S.I.=p脳r脳t100

where it p is the principal, ris the rate and tis the time.

02

Step 2. Form the equation.

Let interest at 5%be $x.

Therefore, investment at 8%is $30000鈭�x.

Interest on $xis calculated as:

S.I.=p脳r脳t100=x脳5脳1100=5x100

Interest on $30000鈭�x is calculated as:

S.I.=p脳r脳t100=30000鈭�x脳8脳1100=830000鈭�x100

As per the question,

Total interest on the investment is $2100.

The equation can be written as:

5x100+830000鈭�x100=2100

03

Step 3. Solve the equation.

The equation can be solved as follows:

5x100+830000鈭�x100=21005x+830000鈭�x100=21005x+240000鈭�8x100=2100鈭�3x+240000100=2100鈭�3x+240000100脳100=2100脳100

role="math" localid="1648195413717" 鈭�3x+240000=210000鈭�3x+240000鈭�240000=210000鈭�240000鈭�3x=鈭�30003x3=300003x=10000

Investment at 5%=$x=$10,000.

Investment at 5%=$30,000鈭�x=$30,000鈭�10,000=$20,000.

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