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Word Problem - steps to solve

by Sylvia Pepe
(Lancaster, Lancashire, United Kingdom)











































A school has 308 dictionaries. There are 3 infant classes and 4 junior classes. The junior classes need twice as many dictionaries as the infant classes. How many dictionaries can each infant and junior class have?

Please, could you help me to find out the different steps for this problem. I have got the answers but I will not get the steps they have done.

Comments for Word Problem - steps to solve

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Feb 09, 2013
Word Problem
by: Staff


Answer


Part I

To answer this question, you will be solving a system of two linear equations.

x = number of dictionaries for each infant class

y = number of dictionaries for each junior class

total number of dictionaries = 308

1st equation:

Use this part of the problem statement to develop the 1st equation:

A school has 308 dictionaries.

There are 3 infant classes and 4 junior classes.


number of dictionaries given to infant classes
+ number of dictionaries given to junior classes
= total number of dictionaries

number of dictionaries given to infant classes
+ number of dictionaries given to junior classes
= 308

(number of infant classes) * x
+ (number of junior classes) * y
= 308


3 * x
+ 4 * y
= 308

3 x + 4 y = 308

2nd equation:

Use this part of the problem statement to develop the 2nd equation:

The junior classes need twice as many dictionaries as the infant classes.
(each junior class will need twice as many dictionaries as each individual infant class)

y = 2x

(number of dictionaries for each junior class)
= 2 * (number of dictionaries for each infant class)


y
= 2 * x


y = 2 x


System of Equations you must solve

1st equation:

3 x + 4 y = 308

2nd equation

y = 2 x


Solving for x and y

This problem can be solved using either the substitution of elimination methods.

I am going to demonstrate the solution using the substitution method.

1st equation

3 x + 4 y = 308

since y = 2 x, substitute 2 x wherever y appears in the 1st equation

3 x + 4 * (2x) = 308

3 x + 8 x = 308

now, solve for x

3 x + 8 x = 308

11 x = 308

11 x / 11= 308 / 11

x * (11 / 11)= 308 / 11

x * (1)= 308 / 11

x = 308 / 11

x = 28 dictionaries

since you now know that x = 28, substitute 28 wherever x appears in the 1st equation

3 x + 4 y = 308

3 * 28 + 4 y = 308

84 + 4 y = 308



---------------------------------------------------------------

Feb 09, 2013
Word Problem
by: Staff


---------------------------------------------------------------


Part II

complete the problem by solving for y

84 + 4 y = 308

84 + 4 y - 84 = 308 - 84

4 y + 84 - 84 = 308 - 84

4 y + 0 = 308 - 84

4 y = 308 - 84

4 y = 224

4 y / 4 = 224 / 4

y * (4 / 4) = 224 / 4

y * (1) = 224 / 4

y = 224 / 4

y = 56 dictionaries

Final Answer:

x (infant class) = 28 dictionaries
y (junior class) = 56 dictionaries


This system of equations can also be solved graphically

Solve 2 equations graphically




----------------------------------------------------
Check the result for accuracy

x = 28 dictionaries

y = 56 dictionaries

1st equation:

3 x + 4 y = 308

3 * 28 + 4 * 56 = 308

84 + 224 = 308

308 = 308, OK

2nd equation:

y = 2 x

56 = 2 * 28

56 = 56, OK





Thanks for writing.

Staff
www.solving-math-problems.com



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