MTH 10905Algebra

SOLVING APPLICATION PROBLEMS

CHAPTER 3 SECTION 2

Use the Problem Solving Procedure

To solve application problems you must answer the question asked.

  We often translate into mathematically terms without realizing it.  For example: You need three cups of milk for a recipe. Your

measuring cup holds 2 cups. You reason that you will need one additional cup.

Let x = additional cups needed2 cups + additional = total2 + x = 3

Solvex = 3 – 2 x = 1 we will need one additional cup.

Use the Problem Solving Procedure

Five-step problem solving procedure:

1. Understand the Problem – Identify the quantity or quantities you are being asked to find.

2. Translate the problem into mathematical language (express the problem as an equation).

1. Choose a variable to represent one quantity, write down exactly what it represents.

2. Using this information write the equation that represents the application.

 3. Carry out the mathematical calculations (solve the equation).

 4. Check the answer (using the original application).

 5. Answer the question asked.

Setup and Solve Number Application Problems

Exp: Four subtracted from three times a number is 11. Find the number.

1. What are we asked to do?

2. Translate the problem.

3. Write the equation.

4. Solve:5. Check: 3x – 4 = 11

3(5) – 4 = 11 15 – 4 = 11

11 = 11

1. Find an unknown number

2. Let x = the unknown number.

3. 3x – 4 = 11

4. 3x – 4 = 11 3x – 4 + 4 =

11 + 4 3x = 15 x = 15/3 = 5

The number is 5

Setup and Solve Number Application Problems

Exp: The difference of two numbers is 16. Find the two numbers if the larger number is 2 less than the 4 times the smaller.

Let x = smaller number 4x – 2 = larger number

(4x – 2) – x = 16 Check: 4x – 2 – x = 16 4x – 2 – x = 16 (4)(6) – 2 – 6 = 16 3x – 2 = 16 24 – 2 – 6 = 16 3x = 18 22 – 6 = 16 x = 18/2 = 6 22 = 22

x = 6 smaller number 4x – 2= (4)(6) – 2 = 22 larger number

Setup and Solve Number Application Problems

Exp: Carol is older than Liz. Carol is four years older than 3 times Liz’s age. The difference between Carol’s and Liz’s age is 10 years. Determine Liz’s age.

Let x = Liz’s age

3x + 4 = Carol’s age

(3x + 4) – x = 10

3x + 4 – x = 10

2x + 4 = 10

2x = 6

x = 6/2 = 3

Liz is 3 years old and Carol is 3(3) + 4 = 9 + 4 = 13 years old

Setup and Solve Number Application Problems

Exp: A company presently has a cash reserve of $30,000. It plans to add $2,500 a month to the reserve until the reserve reaches $55,000. How long will it take the company to reach its goal?

Let x = # of months2,500x = amount for x months

30,000 + 2,500x = 55,000 2,500x = 55,000 – 30,000 2,500x = 25,000 x = 25,000/2,500 = 10

It will take the company 10 months to reach its goal.

Setup and Solve Application Problems involving Money

Exp: A truck rental cost $42 a day plus 24 cents a mile. If the total cost for 1 day rental is $63.60 how many miles were driven?

Let x = number of miles0.24x = cost for x miles

 42 + 0.24x = 63.60 0.24x = 63.60 – 42 0.24x = 21.60 x = 21.60/0.24 = 90

The mileage driven was 90.

Setup and Solve Application Problems involving Money

Exp: The cost of having a load of rubbish picked up by Waste Management is $49 plus 30 cents per pound of rubbish. The cost of having rubbish picked up by Sun City Disposal is $89 plus 10 cents per pound of rubbish. How many pounds of rubbish would need to be picked up to make the cost of both pickups the same?

49 + 0.30x = Waste Management – Less than 200 lbs pick this one

89 + 0.10x = Sun City Disposal – More than 200 lbs pick this one

  49 + 0.30x = 89 + 0.10x0.30x – 0.10x = 89 – 49 0.20x = 40 x = 200

You would need to have 200 lbs of rubbish removed to have equal cost.

Setup and Solve Applications Concerning Percents

Exp: The cost a meal and a 7% tax is $16.26. Find the cost of the meal before tax.

x = cost of meal before tax0.07x = tax on meal

 x + 0.07x = 16.26 1.07x = 16.26

x = 15.20

The cost of the meal before tax was $15.20.

Setup and Solve Applications Concerning Percents

Exp: The number of people who signed up for the company picnic this year is 10% greater than the number who signed up for the last year’s picnic. If 253 people signed up for this year’s picnic, find the number of people who signed up for last years picnic.

x = number who signed up last year

0.10x = amount of increase

x + 0.10x = 253

  1.10x = 253

x = 230

The number of people who signed up for last years picnic was 230.

Setup and Solve Applications Concerning Percents

Exp: The salary plan is $30,000 a year plus 6% commission of sales. A second plan is $40,000 a year plus 4% commission of sales. At what sales will the two plans give the same salary.

Let x = amount of sales30,000 + 0.06x = first plan – Take this job if more than

$500,00040,000 + 0.04x = second plan – Take this job if less than

$500,000

30,000 + 0.06x = 40,000 + 0.04x   0.06x – 0.04x = 40,000 – 30,000

0.02x = 10,000x = 500,000

You need to sale $500,000 in order for the plans to be equal.

HOMEWORK 3.2

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