SOLUTION: the sum of two numbers is 56. one third of the first number plus one fourth of the second number is 16. find the numbers. please give solution in variables x and y. use also for

Question 625855: the sum of two numbers is 56. one third of the first number plus one fourth of the second number is 16. find the numbers.
please give solution in variables x and y. use also formula and explain clearly thanks..
Answer by NewtonMathCenter(2) (Show Source): You can put this solution on YOUR website!
Let x=first number and y=second number.
The sum of two numbers is 56 can be represented as x+y=56.
One third of the first number plus one fourth of the second number is 16 can be written as (1/3)x+(1/4)y=16. Remember of represents multiplication.
Now we can solve this system of equations by either substitution or elimination. I will do elimination. Thus I will multiply the second equation by 12, the lowest common denominator, to eliminate all of the fractions:) We then get
4x+3y=192. I will now multiply the first equation by -3 so we can add the two equations and eliminate the y variable. We then get -3x-3y=-168. Now add the two equations:
4x+3y=192
-3x-3y=-168
x=24
To solve for y, substitute the x into any original equation:
x+y=56
24+y=56
y=32 by subtracting 24 from both sides.
Now you can check your answer:
24+32=56 yes
(1/3)24+(1/4)32=16 yes
Yay:)

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