If two numbers are in the ratio of 5:3 .If their difference is 40. Find the two numbers .
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Answers
let the numbers be 5x and 3x
5x - 3x = 40
2x = 40
x = 20
therefore, two numbers = 100 and 60
Answer:
x/y = 3/5
x-y = 40
Solve for x in the second equation:
x = y + 40
Now substitute for x in the first equation:
x/y = 3/5
x = (y+40)
(y+40)/y = 3/5
Multiply both sides by 5y to eliminate both denominators:
5(y+40) = 3y
Distribute the term to the parentheses on the left:
5y + 200 = 3y
Subtract 3y from both sides:
2y + 200 = 0
Subtract 200 from both sides:
2y = -200
divide by 2:
y = -100
Substitute for y in the other value of x:
x = y + 40
y = -100
x = -100 + 40
x = -60
So far we’ve found that y = - 100 and x = -60. Prove these are correct by substituting for y in the first equation:
x/y = 3/5
x = -60
y = -100
-60/-100 = 3/5
Reduce the fraction on the left with the GCF of 20:
-20*3/-20*5 = 3/5
Divide away the -20’s:
3/5 = 3/5
So x = -60 and y = -100.