Question

The sum of two numbers is 900. If 20% of bigger number is equal to 25% of the smaller number, find the numbers.​​

Answer 1

Answer:

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: Now we solve this for y. First we simplify:

20(900 - y) = 25y

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.