Question 826836: The sum of two numbers is 900. If 20%of one number is equal to 25% of the other. find the numbers.
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Let x = one number and y = the other number. Then "The sum of two numbers is 900." translates into:
x + y = 900
And "20%of one number is equal to 25% of the other" translates into:
0.20*x = 0.25*y
(Note that the percents have been changed to a decimal. Do not use percents in equations. Use the decimal or fractional equivalent!)
Now we have a system of two equations in two variables:
x + y = 900
0.20*x = 0.25*y
To make things simpler, I will multiply both sides of the second equation by 100 (to get rid of the decimals. Now our system is:
x + y = 900
20x = 25y
You have probably learned at least two ways to solve such a system. One of these methods, usually one of the first ones taught, is the Substitution Method. I will solve the first equation for x. Subtracting y from each side we get:
x = 900 - y
Substituting this expression for x into the other equation we get:
20(900 - y) = 25y
Now we solve this for y. First we simplify:
18000 - 20y = 25y
Adding 20y to each side:
18000 = 45y
Dividing by 45:
18000/45 = y
which reduces to:
400 = y
We're almost but not quite done. We need to find x, too. For this we use the value we found for y and one of the two-variable equations:
x + y = 900
x + (400) = 900
x = 500
So the two numbers are 400 and 500.
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