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

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