Question

The sum of two positive numbers is 55 times their difference. What is the ratio of the larger number to the smaller number?

Answer 1

11 * 5 = 55.

In this case 5 would be the smaller number and 11 would be the bigger number.
those two numbers are our ratio's, The sum of them combined is 55.

i hope this helped you.

Answer 2

So x and y
sum means add
difference means subtract
so we have
x+y=55 times (x-y)
use distributiver property which is
a(b-c)=ab-ac so
distribute 55(x-y)
55(x-y)=55x-55y

so we have
x+y=55x-55y
add 55y to boh sides
x+56y=55x
subtract x from both sides
56y=54x
divide both sides by 2
28y=27x
to find the ratio, switch the numbers around
ratio of y:x=27:28
therefor x is the greater number
ratio of larger to smaler is
28:27