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A group of children were on a bus. Three children got off the bus at the first stop. At the next stop, 1212 kids got on the bus. There are now twice as many kids on the bus as there were at the start. How many kids are on the bus?

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Q. A group of children were on a bus. Three children got off the bus at the first stop. At the next stop, 1212 kids got on the bus. There are now twice as many kids on the bus as there were at the start. How many kids are on the bus?
  1. Denote number of children: Let's denote the number of children on the bus at the start as xx. According to the problem, three children got off the bus at the first stop. So, the number of children on the bus after the first stop is x3x - 3.
  2. First stop: Three children off: At the next stop, 1212 kids got on the bus. So, the number of children on the bus after the second stop is (x3)+12(x - 3) + 12.
  3. Second stop: Twelve kids on: The problem states that there are now twice as many kids on the bus as there were at the start. This means that after the second stop, the number of children on the bus is 2x2x. So, we can set up the equation (x3)+12=2x(x - 3) + 12 = 2x.
  4. Equation setup and simplification: Now, let's solve the equation for xx. First, we simplify the left side of the equation: x3+12=x+9x - 3 + 12 = x + 9. So, the equation now is x+9=2xx + 9 = 2x.
  5. Solve for x: To find the value of xx, we subtract xx from both sides of the equation: x+9x=2xxx + 9 - x = 2x - x, which simplifies to 9=x9 = x.
  6. Final number of kids: Now that we have the value of xx, which is 99, we can find out how many kids are on the bus after the stops. Since there are twice as many kids on the bus as there were at the start, we multiply xx by 22: 2×9=182 \times 9 = 18.

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