Question

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?

Select one:
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

Answer 1

a=adult
c=children
total lumber=30
total number=adults+children
a+c=30

total cost=50
total cost=acost+ccost

acost=a times cost per adult=a times 3=3a
ccost=c times cost per child=c tiems 1=1c=c
total cost=3a+c
50=3a+c

equiaotn are
a+c=30
3a+c=50
multiplyu first by -1 and add
3a-a+c-c=50-30
2a=20
a=10
sub
10+c=30
c=20

answer is A

Answer 2

a=number of adults
c=number of children
we can suggest this system of equation:

a+c=30
3a+c=50

We can solve this system of equations by substitution method.
a=30-c

3(30-c)+c=50
90-3c+c=50
-2c=50-90
-2c=-40
c=-40/-2=20

a=30-20=10

Answer:
a. 20 children and 10 adults
Equation 1:    a+c=30
Equation 2:  3a+c=50