# 3.1 Use a problem-solving strategy  (Page 6/8)

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According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,500. This was$1,500 less than 6 times the cost in 1975. What was the average cost of a car in 1975?

$5,000 U.S. Census data shows that the median price of new home in the United States in November 2014 was$280,900. This was $10,700 more than 14 times the price in November 1964. What was the median price of a new home in November 1964?$19,300

## Key concepts

• Problem-Solving Strategy
1. Read the problem. Make sure all the words and ideas are understood.
2. Identify what we are looking for.
3. Name what we are looking for. Choose a variable to represent that quantity.
4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.
5. Solve the equation using good algebra techniques.
6. Check the answer in the problem and make sure it makes sense.
7. Answer the question with a complete sentence.
• Consecutive Integers
Consecutive integers are integers that immediately follow each other.
$\begin{array}{cccc}\hfill n\hfill & & & {1}^{\text{st}}\phantom{\rule{0.2em}{0ex}}\text{integer}\hfill \\ \hfill n+1\hfill & & & {2}^{\text{nd}}\phantom{\rule{0.2em}{0ex}}\text{integer consecutive integer}\hfill \\ \hfill n+2\hfill & & & {3}^{\text{rd}}\phantom{\rule{0.2em}{0ex}}\text{consecutive integer . . . etc.}\hfill \end{array}$

Consecutive even integers are even integers that immediately follow one another.
$\begin{array}{cccc}\hfill n\hfill & & & {1}^{\text{st}}\phantom{\rule{0.2em}{0ex}}\text{integer}\hfill \\ \hfill n+2\hfill & & & {2}^{\text{nd}}\phantom{\rule{0.2em}{0ex}}\text{integer consecutive integer}\hfill \\ \hfill n+4\hfill & & & {3}^{\text{rd}}\phantom{\rule{0.2em}{0ex}}\text{consecutive integer . . . etc.}\hfill \end{array}$

Consecutive odd integers are odd integers that immediately follow one another.
$\begin{array}{cccc}\hfill n\hfill & & & {1}^{\text{st}}\phantom{\rule{0.2em}{0ex}}\text{integer}\hfill \\ \hfill n+2\hfill & & & {2}^{\text{nd}}\phantom{\rule{0.2em}{0ex}}\text{integer consecutive integer}\hfill \\ \hfill n+4\hfill & & & {3}^{\text{rd}}\phantom{\rule{0.2em}{0ex}}\text{consecutive integer . . . etc.}\hfill \end{array}$

## Practice makes perfect

Use the Approach Word Problems with a Positive Attitude

In the following exercises, prepare the lists described.

List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.

List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.

Use a Problem-Solving Strategy for Word Problems

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

Two-thirds of the children in the fourth-grade class are girls. If there are 20 girls, what is the total number of children in the class?

30

Three-fifths of the members of the school choir are women. If there are 24 women, what is the total number of choir members?

Zachary has 25 country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?

125

One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag?

There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.

6

There are 18 Cub Scouts in Pack 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.

A veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic equation A=x(100−2x) gives the area, A , of the dog run for the length, x , of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area, and then find the maximum area of the dog run.
ggfcc
Mike
Washing his dad’s car alone, eight year old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
1,75hrs
Mike
I'm going to guess. Divide Levi's time by 2. Then divide 1 hour by 2. 1.25 + 0.5 = 1.3?
John
Oops I mean 1.75
John
I'm guessing this because since I have divide 1 hour by 2, I have to do the same for the 2.5 hours it takes Levi by himself.
John
Drew burned 1,800 calories Friday playing 1 hour of basketball and canoeing for 2 hours. On Saturday, he spent 2 hours playing basketball and 3 hours canoeing and burned 3,200 calories. How many calories did he burn per hour when playing basketball?
Brandon has a cup of quarters and dimes with a total value of $3.80. The number of quarters is four less than twice the number of dimes. How many quarters and how many dimes does Brandon have? Kendra Reply Tickets to a Broadway show cost$35 for adults and $15 for children. The total receipts for 1650 tickets at one performance were$47,150. How many adult and how many child tickets were sold?
825
Carol
Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received$4,500 in interest in one year? How do I do this
how to square
easiest way to find the square root of a large number?
Jackie
the accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery set up a linear system whose solution provides the unknown flow rates (b) solve the system for the unknown flow rates (c) find the flow rates and directions of flow if x4=50and x6=0
What is observation
I'm confused by the question. Can you describe or explain the math question it pertains to?
Melissa
there is no math to it because all you use is your vision or gaze to the sorrounding areas
Cesarp
Teegan likes to play golf. He has budgeted $60 next month for the driving range. It costs him$10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?
5 times max
Anton
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 1/3 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
35 min
Debra
Carmen wants to tile the floor of his house. He will need 1,000 square feet of tile. He will do most of the floor with a tile that costs $1.50 per square foot, but also wants to use an accent tile that costs$9.00 per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be $3 per square foot? Parker Reply what you wanna get Cesar 800 sq. ft @$1.50 & 200 sq. ft @ $9.00 Marco Geneva treated her parents to dinner at their favorite restaurant. The bill was$74.25. Geneva wants to leave 16 % of the total - bill as a tip. How much should the tip be?
74.25 × .16 then get the total and that will be your tip
David
$74.25 x 0.16 =$11.88 total bill: $74.25 +$11.88 = $86.13 ericka yes and tip 16% will be$11.88
David
what is the shorter way to do it
Priam has dimes and pennies in a cup holder in his car. The total value of the coins is \$4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup?