# Learn procedures for solving applied problems.

### Procedure for Solving Applied Problems

Step 1  Read the problem as many times as needed to understand it thoroughly. Pay close attention to the questions asked to help identify the quantity the variable should represent.

Step 2  Assign a variable to represent the quantity you are looking for, and, when necessary, express all other unknown quantities in terms of this variable. Frequently, it is helpful to draw a diagram to illustrate the problem or to set up a table to organize the information.

Step 3  Write an equation that describes the situation.

Step 4  Solve the equation.

Step 6  Check the answer against the description of the original problem (not just the equation solved in step 4).

#### example:

Tyrick invests \$15,000, some in stocks and the rest in bonds. If he invests twice as much in stocks as he does in bonds, how much does he invest in each?

#### Solution

##### Step 1

Let x = the amount invested in stocks. The rest of the \$15,000 investment (\$15,000 – x) is invested in bonds. We have one more important piece of information to use:

##### Step 2.

Amount invested in stocks, x = Twice the amount invested in bonds, 15,000 –x

##### Step 3.

x=2(15,000-x) Replace the verbal description with algebraic expressions.

##### Step 4.

x= 30,000-2x  Distributive property

3x=30,000  Add 2x to both sides.

x=10,000  Divide both sides by 3.

##### Step 5

Tyrick invests \$10,000 in stocks and \$15,000 – \$10,000 = \$5000 in bonds.

##### Step 6

Tyrick’s total investment is \$10,000 + \$5000 = \$15,000, and \$10,000 (stocks) is twice \$5,000 (bonds).

referrence : About M. syoiful bachri