SOLUTION: the sum of two numbers is 45 and their quotient is 500 what are the two numbers

Question 1168974: the sum of two numbers is 45 and their quotient is 500 what are the two numbers

Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Let x and y be the two unknown numbers. Let's make x smaller than y, meaning x < y.

The sum of two numbers is 45 tells us: x+y = 45

Their quotient is 500 means: y/x = 500
We wouldn't say x/y = 500 because the larger number should go on top (so the quotient is larger than 1).

Solve for y in the equation y/x = 500 to get y = 500x. You multiply both sides by x to isolate y.

Since y = 500x, we can replace y in the first equation with 500x and solve for x

x+y = 45
x+500x = 45
1x+500x = 45
501x = 45
x = 45/501
x = (15*3)/(167*3)
x = 15/167 is one of the numbers

Use this to find the value of y
y = 500x
y = 500*(15/167)
y = (500/1)*(15/167)
y = (500*15)/(1*167)
y = 7500/167 is the other number

The two numbers are therefore 15/167 and 7500/167

Use a calculator to find that
15/167 = 0.08982035928143
7500/167 = 44.9101796407186
both decimal values are approximate.

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