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Math - Solve Word Problem

by Czyrell May Ebe
(Batangas City)











































The larger of two numbers is six more than six times the smaller number. The larger number is also one hundred twenty-two more than two times the smaller number. What are the numbers?

Let l be the larger number
Let s be the smaller number

Comments for Math - Solve Word Problem

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Jul 15, 2011
Solve Word Problem
by: Staff


The question:

by Czyrell May Ebe
(Batangas City)

The larger of two numbers is six more than six times the smaller number. The larger number is also one hundred twenty-two more than two times the smaller number. What are the numbers?

Let l be the larger number
Let s be the smaller number


The answer:

L = large number
S = small number

The larger of two numbers is six more than six times the smaller number.

L = 6S + 6

The larger number is also one hundred twenty-two more than two times the smaller number.

L = 2S + 122

We now have two equations with two unknowns:

L = 6S + 6
L = 2S + 122


Solve for the variable “S” using the addition/subtraction method.

Eliminate the unknown variable “L” by subtracting the second equation from the first equation:

L = 6S + 6
-(L = 2S + 122)

L = 6S + 6
-L = -2S - 122
------------------
L - L = 6S - 2S + 6 - 122


0 = 6S - 2S + 6 - 122

0 = 4S + 6 – 122

0 = 4S -116


Add 116 to each side of the equation

0 = 4S -116

0 + 116 = 4S -116 + 116
116 = 4S -116 + 116

116 = 4S + 0

116 = 4S


To eliminate the 4 from the 4S, divide each side of the equation by 4

4S = 116

4S/4 = 116/4

S*(4/4) = 116/4

S*(1) = 116/4

S = 116/4

S = 29


Solve for “L” by substituting the numerical value of “S” (S = 29) into either one of the original equations

L = 6S + 6

L = 6*29 + 6

L = 174 + 6

L = 180


The final answer is: S (the smaller number) = 29; L (the larger number) = 180



Check the work. Substitute the numerical values of both S and L in the original equations:

L = 6S + 6

180 = 6*29 + 6

180 = 174 + 6

180 = 180, OK



L = 2S + 122

180 = 2*29 + 122

180 = 58 + 122

180 = 180, OK



Thanks for writing.

Staff
www.solving-math-problems.com



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