In mathematics, solving problems is an important activity. Any problem can be solved using a problem-solving plan like the one below.
1.
Explore
Read the problem carefully.
Identify the information that
is given and determine
what you need to find.
2.
Plan
Select a strategy for solving
the problem. Some strategies
are shown at the right. If
possible, estimate what you think
the answer should be before
solving the problem.
3.
Solve
Use your strategy to solve the problem.
You may have to
choose a variable for the unknown,
and then write an
expression. Be sure to answer the
question.
4.
Examine
Check your answer. Does it make sense?
Is it reasonably
close to your estimate?
One
important problem-solving strategy is using an equation. An equation that
states a rule for the ralationship between quantities is called a formula.
Money in a
bank account earns interest. You find simple interest by using the
formula I = prt.
I = interest
p = principal, or amount deposited
r = interest rate, written as a
decimal
t =
time in years
Example
Savings Link
1. Suppose
you deposit $220 into an account that pays 3% simple interest. How much money
would you have in the account after five years?
Alternative Solutions :
Explore What do you know?
• The amount of money deposited is $220.
• The interest rate is 3% or 0.03.
• The time is 5 years.
What do you need to find?
• the amount of money, including interest, at the end of
five years
Plan
What is the best strategy to use?Use the formula I prt and
substitute the known values.
Add this amount to the original deposit.
Estimate: 1% of $220 is $2.20. So, 3% of $220 is about 3 $2
or $6 per year. This will be $30 in five years. You should
have approximately 220 30 or $250 in
five years.
Solve I = prt Interest
Formula
I = 220 ⋅ 0.03 ⋅ 5 or 33 p = 220, r = 0.03,
and t = 5
You will earn $33 in interest, so the total amount after five
years is $220 $33 or $253.
Examine Is your answer close to your estimate?
Yes, $253
is close to $250, so the answer is reasonable.
Another important problem-solving strategy is using a
model. In the activity below, you will use a model to find a formula for
the surface area of a rectangular box.
Example
Money Link
2. How many ways can you make 25¢ using dimes, nickels, and pennies?
Alternative Solutions :
Explore A quarter is
worth 25¢. How many ways can you
make 25¢
without using a quarter?
Plan Make a
chart listing every possible combination.
Solve 
There are 12 ways to make 25¢.
Examine Check that each
combination totals 25¢ and that
there
are no other possible combinations. The solution
checks.
The chart below summarizes the properties of numbers. The
properties are useful when you are solving problems.
Sumber
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