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Word Problem - Use the five steps for solving to answer

by Hope Floyd
(Baton Rouge, La(U.S.A))











































Use the five steps for problem solving to answer the following question. Please show all of your work.

The bowling alley on Wedge Street charges $5.50 for shoe rental plus $2.50 per game. The bowling alley on Lawrence Street charges $4 for shoe rental plus $3.00 per game. If one person rents a pair of shoes to bowl, how many games should they bowl to make the bowling alley on Wedge Street cheaper than the bowling alley on Lawrence Street?

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Jul 24, 2011
Word Problem ā€“ Break Even Value
by: Staff


The question:

Use the five steps for problem solving to answer the following question. Please show all of your work.

The bowling alley on Wedge Street charges $5.50 for shoe rental plus $2.50 per game. The bowling alley on Lawrence Street charges $4 for shoe rental plus $3.00 per game. If one person rents a pair of shoes to bowl, how many games should they bowl to make the bowling alley on Wedge Street cheaper than the bowling alley on Lawrence Street?


The answer:

The five steps are:

1. Understand what the problem is asking you to do
2. Identify the information provided (known and unknown information)
3. Write (or rewrite) the known and unknown information using mathematical notation (rather than sentences)
4. Solve the problem
5. Check your answer


Applying these 5 steps to your problem:

1. Understand what the problem is asking you to do

(Read the last sentence in the problem statement.)

How many games should a person bowl to make the bowling alley on Wedge Street cheaper than the bowling alley on Lawrence Street?


2. Identify the information provided (known and unknown information)

Known Information

- One person rents a pair of shoes to bowl in each case.

- The bowling alley on Wedge Street charges $5.50 for shoe rental plus $2.50 per game.

- The bowling alley on Lawrence Street charges $4 for shoe rental plus $3.00 per game.

Unknown Information

- Number of games bowled


3. Write (or rewrite) the known and unknown information using mathematical notation (rather than sentences)

W = cost of bowling at Wedge Street

L = cost of bowling at Lawrence Street

G = number of games bowled


The equation for the cost of bowling at Wedge Street is:

W = $5.50 + $2.50 * G


The equation for the cost of bowling at Lawrence Street is:

L = $4.00 + $3.00 * G



Cost of bowling at Wedge Street less than the cost of Lawrence Street

W < L

$5.50 + $2.50 * G < $4.00 + $3.00 * G



4. Solve the equation

Solve for G

5.50 + 2.50 * G < 4.00 + 3.00 * G

Subtract 4.00 from each side of the equation

5.50 - 4.00 + 2.50 * G < 4.00 - 4.00 + 3.00 * G

5.50 - 4.00 + 2.50 * G < 0 + 3.00 * G

5.50 - 4.00 + 2.50 * G < 3.00 * G

1.50 + 2.50 * G < 3.00 * G

Subtract 2.50 * G from each side of the equation


1.50 + 2.50 * G - 2.50 * G < 3.00 * G - 2.50 * G

1.50 + 0 < 3.00 * G - 2.50 * G

1.50 < 3.00 * G - 2.50 * G

1.50 < 0.50 * G


Divide each side of the equation by 0.50

1.50/0.50 < 0.50 * G/0.50

3 < 0.50 * G/0.50

3 < G * (0.50/0.50)

3 < G * (1)

3 < G


The final answer is: more than 3 games.



5. Check the answer

Substitute the numerical value of ā€œGā€ in the original equation:


In this case we are going to use a value of 3 (rather than >3) to verify the break even value.


$5.50 + $2.50 * G < $4.00 + $3.00 * G

$5.50 + $2.50 * 3 = $4.00 + $3.00 * 3

$5.50 + $7.50 = $4.00 + $3.00 * 3

$13.00 = $4.00 + $3.00 * 3

$13.00 = $4.00 + $9.00

$13.00 = $13.00, correct






Thanks for writing.

Staff
www.solving-math-problems.com


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