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one number is 21 less then another number. if the sum of the two numbers is 91 find the two numbers

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Feb 24, 2010
Math - Solving a 2 variable equation
by: Staff


The problem


one number is 21 less then another number. if the sum of the two numbers is 91 find the two numbers



The solution

Assign variable names to the two numbers (I have used X & Y, but you can assign any variable name you wish):

X = 1st number, and Y = 2nd number


Write the two equations:

1st equation: one number is 21 less then another number: X = Y - 21

2nd equation: the sum of the two numbers is 91: X + Y = 91



Solve the two equations for X & Y (substitution is probably the easiest way):

X = Y – 21 - 1st equation
X + Y = 91 - 2nd equation

The first equation shows that X and Y – 21 are equivalent (they are equal, right)

Replace the X in the 2nd equation with Y – 21


(Y – 21) + Y = 91


Solve for Y using the 2nd equation

(Y – 21) + Y = 91

Y – 21 + Y = 91

Y + Y – 21 = 91

2Y – 21 = 91

2Y – 21 + 21 = 91 + 21

2Y + 0 = 112

2Y = 112

2Y/2 = 112/2

Y = 56


Solve for X using the 1st equation by substituting the number 56 for the variable Y


X = Y – 21

X = 56 – 21

X = 35


The final answer to your question is:

X = 35
Y = 56

Note that X is exactly 21 less than Y,
And the sum of X & Y does equal 91.




Staff
www.solving-math-problems.com


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