When 3 times a certain number n is added to 6 the sum is 20 more than the original number What is number n?

Answer 1

You can use algebra to solve this function once you put the quantities involved in symbolic forms. "3 times a certain number n" is written 3*n or 3n. the question then states that this quantity is added to 6, so we have the quantity 3n + 6. It then says that 3n + 6 is 20 more than the original number n, so 3n + 6 = 20 + n. We can now manipulate this equation using algebra to get an equation of the form n = R where R is an expression that does not involve n:

# 3n + 6 = 20 + n # 3n + 6 + (-n) = 20 + n + (-n) [[Adding the same constant (-n) to both sides maintains equality]] # 2n + 6 = 20 [[n + (-n) = 0 by definition]] # 2n + 6 + (-6) = 20 + (-6) # 2n = 14 # 2n*(1/2) = 14*(1/2) [[We need to get rid of that 2, and multiplying both sides by the same constant preserves equality]] # n = 7

So the original number must have been 7.