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Question 1017846: two numbers are in the ratio of 4:5. the value of the large number is 35 more than the smaller number, then the product of the numbers is ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let the numbers be x and y.
the ratio between x and y is x/y = 4/5.
the value of the larger number is 35 more than the smaller number.
if the ratio of x/y = 4/5, then y must be the larger number.
how do you know that?
solve the equation for x to get x = 4/5 * y.
since the fraction is less than 1, x must be smaller than y.
the problem states that the larger number is equal to 35 more than the smaller number.
this means that y = x + 35.
since y = x + 35, the ratio of x/y = 4/5 becomes x/(x+35) = 4/5
cross multiply to get 5x = 4 * (x+35)
simplify to get 5x = 4x + 140
subtract x from both sides of the equation to get 5x - 4x = 4x + 140 - 4x
simplify to get x = 140.
since y = x + 35, then y must be equal to 175.
you have x = 140 and y = 175.
the ratio between x and y is 4/5, so you get x/y = 4/5 becomes 140/175 = 4/5.
since 4 goes into 140 thirty five times, then divide numerator and denominator of 140/175 by 35 to get:
(140/35) / (175/35) = 4/5.
the ratio holds.
x = 140 and y = 175.
multiply x and y together to get 140 * 175 = 24500.
the product of the numbers is 24,500.
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