If the denominator of 4/7 is increased by a number and the numerator is doubled, the result is 1. Find the number.

If the denominator of 4/7 is increased by some number x, then we have 4 / (7+x)

If the numerator is doubled, then we now have 8 / (7+x) because 4*2 = 8

Set that new fraction 8 / (7+x) equal to 1 and solve for x

8 / (7+x) = 1

8 = (7+x) * 1 ... multiply both sides by (7+x)

8 = 7+x

7+x = 8

x+7 = 8

x = 8-7 ... subtract 7 from both sides

x = 1

Answer: 1

(note: 4/7 will turn into 8/8 after adding the number 1 to the denominator and doubling the numerator. The fraction 8/8 reduces to 1)