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40 foot beam is to be cut in two

by cece
(CA)











































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

A 40 foot beam is to be cut in two. If one portion is one third the length of the other portion, what are the two lengths of the portions

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Jun 01, 2011
Math - Word Problem
by: Staff


The question:

by cece
(CA)


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

A 40 foot beam is to be cut in two. If one portion is one third the length of the other portion, what are the two lengths of the portions?


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 part of the second sentence in the problem statement.)

What are the two lengths of the portions?


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

A 40 foot beam is to be cut in two. If one portion is one third the length of the other portion

Known Information

- length of beam = 40 feet

- one portion is one third the length of the other portion

Unknown Information

- the two lengths of the portions


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

x = length of first portion

y = length of second portion


The equation for the length of the beam is:

x + y = 40 feet


the equation relating the lengths of the two portions:

x = (1/3)*y



4. Solve the equations

Substitute (1/3)*y for the x in the first equation, and then solve for y:

x + y = 40

(1/3)*y + y = 40


Combine like terms

(1/3)*y + y = 40

(1/3)*y + (3/3)*y = 40

(4/3)*y = 40


Multiply each side of the equation by (3/4)

(4/3)*y = 40

(3/4)*(4/3)*y = (3/4)*(40)

(3/3)*(4/4)*y = (3/4)*(40)

(1)*(1)*y = (3/4)*(40)

y = (3/4)*(40)

y = (3)*(40/4)

y = (3)*(10)

y = 30 feet


Substitute 30 for the y in the first equation, and then solve for x:


x + y = 40

x + 30 = 40

Subtract 30 from each side of the equation

x + 30 = 40

x + 30 - 30 = 40 - 30

x + 0 = 40 - 30

x = 40 - 30

x = 10 feet


the final answer to your question is: the length of one of the portions = 10 feet, and the length of the other portion = 30 feet


5. Check the answer

Substitute all values in the original equation:

x = 10

y = 30

x + y = 40 feet

10 + 30 = 40

40 = 40, OK


10 = (1/3)*30

10 = (30/3)

10 = 10, OK





Thanks for writing.

Staff
www.solving-math-problems.com



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