Question 1168974: the sum of two numbers is 45 and their quotient is 500 what are the two numbers
Answer by math_tutor2020(3817)   (Show Source):
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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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