Often, word problems appear confusing, and it is difficult to know where to begin. Here are some steps that will make solving word problems easier:

- Read the problem.
- Determine what is known and what needs to be found (what is unknown).
- Try a few numbers to get a general idea of what the solution could be.
- Write an equation.
- Solve the equation by inverse operations or by plugging in values.
- Check your solution--does it satisfy the equation? Does it make sense in the context of the problem? (e.g. A length should not be negative.)

*Example 1*: Matt has 12 nickels. All the rest of his coins are dimes. He has just enough money to buy 2 slices of pizza for 95 cents each. How many dimes does he have?

- Read the problem.
- What is known? Matt has 12(5) = 60 cents in nickels. Matt has 2(95) = 190 cents total. What needs to be found? The number of dimes that Matt has.
- Try a few numbers:

5 dimes? 10(5) + 60 = 110.

*Too low.*

10 dimes? 10(10) + 60 = 160.*Still too low.*

20 dimes? 10(20) + 60 = 260.*Too high.*

So we know the answer is between 10 and 20. - Write an equation:
10
*d*+ 60 = 190 where*d*is the number of dimes Matt has. - Solve using inverse operations:

10

*d*+ 60 - 60 = 190 - 60

10*d*= 130

=

*d*= 13 - Check: 10(13) + 60 = 190? Yes. Does 13 dimes make sense in the context of the problem? Yes.

*Example 2*: Jen is shooting free-throws on the basketball court. She makes 85% of her shots. If she makes 51 shots, how many does she miss?

- Read the problem.
- What is known? Jen makes 85% -- or -- of her shots. Jen makes 51 shots. What needs to be found? The number of shots that Jen misses.
- Try a few numbers:

5 shots? = .

*Not enough misses.*

10 shots? = .*Too many misses.*

So we know the answer is between 5 and 10. - Write an equation:
=
where
*x*is the number of misses. - Solve using inverse operations:

=

51() = 51()

51 +*x*= 60

51 +*x*- 51 = 60 - 51

*x*= 9 - Check: = ? Yes. Does 9 shots make sense in the context of the problem? Yes.

Diagram of a Square

- Read the problem.
- What is known? The area of the square is 2 times its perimeter. The formula for area is
*A*=*x*^{2}and the formula for perimeter is*p*= 4*x*. What needs to be found? The length of a side. - Try a few numbers:
*x*= 5 ?*A*= 5^{2}= 25 ,*p*= 4(5) = 20 .*Area too small.*

*x*= 10 ?*A*= 10^{2}= 100 ,*p*= 4(10) = 40 .*Area too large.*

So we know the answer is between 5 and 10. - Write an equation:
*x*^{2}= 2(4*x*) .*x*^{2}= 8*x* - Solve by plugging in values----or by using inverse operations:

=

*x*= 8 - Check:
8
^{2}= 8(8) ? Yes. Does 8 make sense in the context of the problem? Yes.

Take a Study Break!