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

So sum means add
difference means subtract
represent as x and y
x+y=55 times (x-y)
find ratio of numbers
solve for one placeholder and simplify
solve for y
distributiver property a(b-c)=ab-ac
55(x-y)=55x-55y

x+y=55x-55y
add 55y to both sides
x+56y=55x
subtract x from both sides
56y=54x
divide both sides by 56
y=54/56(x)
y=27/28(x)
ratio is 28:27
that happens to be theri falues

so the ratio si 28 to 27