20% of the passengers on a bus were children. After 10 adults got off the bus, the percentage of children on the bus increased to 30%. How many passengers were on the bus in the end?
.2 p = c
.3 (p - 10) = c ... .3 p - 3 = c
.2 p = .3 p - 3
solve for p , then subtract the 10 adults that got off
please put the answer?
To solve this problem, we can start by assigning a variable to represent the total number of passengers on the bus. Let's use "x" for that value.
According to the given information, initially 20% of the passengers were children. So, the number of children on the bus can be calculated by taking 20% of the total number of passengers:
Number of children = 20% * x
Now, after 10 adults got off the bus, the percentage of children increased to 30%. This means that the number of children now represents 30% of the total number of passengers:
Number of children = 30% * (x - 10)
Now we can set up an equation to solve for the value of x:
20% * x = 30% * (x - 10)
To simplify the equation, we can convert the percentages to decimals:
0.2x = 0.3(x - 10)
Distribute on the right side:
0.2x = 0.3x - 3
Subtract 0.3x from both sides:
-0.1x = -3
Divide by -0.1:
x = -3 / -0.1
x = 30
So, there were initially 30 passengers on the bus.