Question 1017846
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.