Chapter Twenty-Three — Word Problems
The Humongous Book of Algebra Problems
Solve the system using elimination.
Alice is currently 20 years old. To determine Mel’s age, substitute y = 20 into
either equation of the system and solve for x.
Mel is currently 45 years old, 25 years older than Alice.
Simple, compound, and continuously compounding
23.9 How much simple interest accrues on a loan of $1,200 at an annual rate of
4.5% over a three-year period?
The formula for simple interest is i = prt, where i is interest, p is the principal,
r is the annual interest rate expressed as a decimal, and t is the length of time
(in years) the principal accrues interest. Substitute p = 1,200, r = 0.045, and t = 3
into the formula to calculate i.
The total accrued interest is $162.
23.10 If you wish to borrow $3,000 from a friend who will charge you simple interest
at an annual rate of 7%, and you cannot exceed $3,300 in total debt. What
is the maximum length of time you have to repay the debt and the accrued
interest? Round the answer to the nearest whole day.
You intend to borrow $3,000 but your total debt cannot exceed $3,300.
Therefore, the maximum total interest you can afford to pay is
$3,300 – $3,000 = $300. Substitute i = 300, p = 3,000, and r = 0.07 into the
simple interest formula to calculate the number of years t it would take to
accrue $300 in interest.
equation by –1, add
the equations, and
solve for y.
you answer the
question posed by
the word problem.
In this case, you’re
supposed to gure
out how much older
Mel is than Alice, so
subtract their ages:
x – y = 45 – 20 = 25.
is the dollar
amount that earns
interest. In this
case, the principal
4.5% into a
decimal, move the
decimal point two
places to the left: