Explanation The first word problem is as follows : A man put $22,000 in a bank 15 years ago. He has earned $21,450 in interest, nearly as much as his initial investment. What was the interest rate that the bank paid him? Simple interest formula is, I = P R T where I = Interest gained P = Principle amount invested R = Rate of interest T = Time duration for which the amount is invested Provided in the problem: I = $ 21 , 450 P = $ 22 , 000 T = 15 years Put the value of I , P , and T in the simple interest formula and find out the interest rate as follows: I = P R T 21 , 450 = 22 , 000 × R × 15 21 , 450 = 330 , 000 R R = 0.065 R = 6.5 % So, the interest rate is R = 6.5 % . The second word problem is as follows : A man invested $15,000 for 10 years at an interest rate of 6% compounded monthly. How much interest has he gained after 10 years? The compound interest formula is A = P ( 1 + r n ) n t where A = Interest gained P = Principle amount invested r = Rate of interest n = Number of times the interest is compounded annually t = Time duration for which the amount is invested Provided in the problem: P = 15 , 000 r = 0.06 n = 12 t = 10 Put the above value in the compound interest formula and simplify as follows: A = P ( 1 + r n ) n t = 15 , 000 ( 1 + 0.06 12 ) 12 × 10 = 15 , 000 ( 1.005 ) 120 = 15 , 000 ( 1.819397 ) So, the amount is $ 27 , 290.95 . The third word problem is as follows : A person has x bitcoins and y ripples. The linear equations concerning the bitcoins and ripples are x + y = 10 and x − y = 2 . What is the number of bitcoins and ripples that the person has? Provided equations are, x + y = 10 …...…... (1) x − y = 2 …...…... (2) Add both the above equations: x + y + ( x − y ) = 10 + 2 2 x = 12 x = 6 Put the value of x in equation (1), simplify as follows: 6 + y = 10 y = 10 − 6 y = 4 The person has 6 bitcoins and 4 ripples

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ISBN: 9781323142707

Author: Blitzer

Publisher: Pearson Custom Publishing

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Chapter 1.3, Problem 92E

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Five-word problems that can be solved using linear equations.

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