number of kids --- x
number of adults -- 52-x
solve for x .....
2x + 3(52-x) = 139
number of adults -- 52-x
solve for x .....
2x + 3(52-x) = 139
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.
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