Question 785049: there are 2 numbers. one number is 0.125 of the other number. their sum is 45. what are the numbers?
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! To solve this problem, let's first translate the three sentences into actual equations. The first sentence states that there are 2 numbers. Let's translate this into math: Since we have two unknown numbers, we will call them x and y.
The next sentence says that one number is .125 of the other number. In other words, x is .125 of y, which can be expressed symbolically as: x = .125y.
The third sentence says that the sum of both numbers is 45. In other words, x + y =45.
To solve, we need to use only ONE of our variables. Since we know that x = .125y, we will substitute .125y for x in our x + y = 45 equation. We will then have: .125y + y = 45
Working with decimals is alot easier if you convert the decimal to a whole number. To convert .125y to a whole number, we need to multiply it by 1000, because that will give us 125y. Remember, since you are dealing with an equation, you must multiply all of the terms by 1000. Doing so gives us:
125y + 1000y = 45000
Next, add the terms on the left of the equation, which gives us: 1125y = 45000
Now, divide both sides of the equation by 1125 so that y will be by itself on the left side of the equation. Doing this gives us: y = 40
We now know that one of our numbers is 40. To find the other number, substitute 40 for y in our x + y = 45 equation: x + 40 = 45.
Subtract 40 from both sides of the equation. This will give us our other number: 5
FINAL ANSWER: 40 and 5 are our two numbers
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