bus tickets cost $3 for an adult and $2 for a child. there are 'a' adults nd 'c' children on a bus. the total number of people on the bus is 52. the total cost of the 52 tickets is $139. find the number of children on the bus.

Let's solve this problem step-by-step.

Step 1: Assign variables
Let's assign variables to the unknown quantities.
- Let 'a' be the number of adults on the bus.
- Let 'c' be the number of children on the bus.

Step 2: Set up equations
Based on the given information, we can set up two equations.
Equation 1: a + c = 52 (Total number of people on the bus)
Equation 2: 3a + 2c = 139 (Total cost of the tickets)

Step 3: Solve the equations
We can solve the system of equations by substitution or elimination method.

Using the substitution method:
From Equation 1, we can express 'a' in terms of 'c' as:
a = 52 - c

Substitute this value of 'a' into Equation 2:
3(52 - c) + 2c = 139
156 - 3c + 2c = 139
156 - c = 139
-c = 139 - 156
-c = -17
c = 17

Step 4: Answer
The number of children on the bus is 17.

To find the number of children on the bus, we can use the information given about the ticket prices and the total number of people and total cost.

Let's break down the problem step by step:

1. Let's assume there are 'a' adults and 'c' children on the bus. According to the problem, the total number of people on the bus is 52. So we have:
a + c = 52 ---(Equation 1)

2. The cost of an adult ticket is $3, and the cost of a child ticket is $2. The total cost of 52 tickets is $139. So we have another equation:
3a + 2c = 139 ---(Equation 2)

Now we have a system of two equations with two variables (a and c). We can solve this system of equations to find the values of a and c.

To solve the system of equations, we can use either substitution or elimination method. Let's use the elimination method in this case:

Multiply equation 1 by 2 to make the coefficients of 'c' the same as equation 2:
2a + 2c = 104 ---(Equation 3)

Now we can subtract equation 3 from equation 2 to eliminate the variable 'c':
(3a + 2c) - (2a + 2c) = 139 - 104
a = 35

Substitute the value of a into equation 1 to find c:
35 + c = 52
c = 52 - 35
c = 17

Therefore, there are 17 children on the bus.

To summarize:
Number of children on the bus = 17

number of kids --- x

number of adults -- 52-x

solve for x .....

2x + 3(52-x) = 139