Question

I think of a number, add 4 to it, multiply by 5 and then take away 6. Finally I divide by 7. I now have the same number I started with. What number did I start with?

Answer 1

Ответ:

7

Пошаговое объяснение:

$\frac{5(x+4)-6}{7} = x \\ \\ 5x + 20 - 6 = 7x\\ \\ 14 = 2x\\ \\ x = 7$

Answer 2

Let's use algebra to solve this problem.

Let the number you started with be "x."

You added 4 to it, so now you have x + 4. Then, you multiplied the result by 5, so you have 5(x + 4). Next, you took away 6, which gives you 5(x + 4) - 6. Finally, you divided by 7, so you have (5(x + 4) - 6) / 7.

According to the problem, this final result is the same as the number you started with, which is x:

x = (5(x + 4) - 6) / 7

Now, let's solve for x:

7x = 5(x + 4) - 6

Distribute 5 on the right side:

7x = 5x + 20 - 6

Combine like terms:

7x = 5x + 14

Subtract 5x from both sides:

2x = 14

Now, divide by 2:

x = 7

So, the number you started with was 7.