A zoo train ride costs $3 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who took the ride was 30, and the total money collected was $50. What was the number of children and the number of adults who took the train ride that day, and which pair of equations can be solved to find the numbers?
Group of answer choices
A 20 children and 10 adults
Equation 1: a + c = 30
Equation 2: 3a + c = 50
B 10 children and 20 adults
Equation 1: a + c = 30
Equation 2: 3a − c = 50
C 20 children and 10 adults
Equation 1: a + c = 30
Equation 2: 3a − c = 50
D 10 children and 20 adults
Equation 1: a + c = 30
Equation 2: 3a + c = 50
Answers
Given:
Total persons who took the ride= $30
Total amount collected= $50
Cost per adult= $3
Cost per child= $1
To find:
1. The number of children and the number of adults who took the train ride that day.
2. Which pair of equations can be solved to find the numbers?
Solution:
We can form two equations using the given information-
Total persons= 30
So, we can write a+c= 30
Also, total amount= 50
So we can write 3a+ c = 50
Now solving both the equations, we get the value of a= 10 and c= 20
The number of adults= 10
The number of children= 20
The equations required are:
Equation 1: a + c = 30
Equation 2: 3a + c = 50.
The number of children and the number of adults who took the train ride that day is 20 and 10.
Step 1: Given data
A zoo train ride costs $3 for adult and $1 for child.
On a certain day, the total number of adults (a) and children (c) who took the ride was 30
Hence equation a + c = 30.--------(1)
Again on the same day total ,money collected was $50.
Hence the equation for money is 3a + c = 50.----------(2)
Step 2: To find
The number of children and the number of adults who took the train ride on that day.
And In the four pair of equation in the question we get first pair in the above step 1. Hence A is correct.
By solving equation (1) & (2)
a + c = 30
3a + c = 50
-2a = -20
a = 10
Hence the total number of adults is 10.
To find the total number of children apply a =10 in the equation (1)
a + c = 30
10 + c = 30
c = 30 - 10 = 20
c = 20
Hence the total number of children is 20.
Therefore, the number of children and the number of adults who took the train ride that day is 20 and 10.
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