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