When 60% of a number is added to the number, the result is 160

Answer 1

We'll call the number "x".

60% of a number = 0.6x

60% of a number, added to the number = 0.6x + x

So 0.6x + x = 160

1.6x = 160

x = 100

Answer 2

Any percentage can be written as that number divided by 100. As a decimal, you find that quotient. You can quickly divide any number by 10 by moving the decimal place to the left for every 0 in that multiple of 10. 100 has 2 zeros, so all you need to do to divide by 100 is to move the decimal place 2 places to the left. Therefore, 60% is .6 as a decimal.

Let's say the number we want to find is x. In word problems, "of" indicates multiplication, so 60% of our number would be .6x.

We then add our number to that, giving us .6x +x

We know the result is 160, so

.6x + x = 160

Since any number multiplied by 1 is itself, that x can be written as 1x.

.6x + 1x = 160

Now, we combine our like terms; we add the numbers in front of the x's (aka coefficients).

(.6 + 1)x = 160

1.6x = 160

We want x by itself. 1.6 is multiplied by our number, so to undo multiplication, we do division. This leaves us with

x = 160/1.6

x=100