A class went on a field trip to see a play. Adult tickets cost $18 each and student tickets cost $12 each. There were 10 more students than adults that went to the play. If the trip cost $240 in all, how many adults and students went to see the play? Write and solve a system of equations by substitution.
a = 4
S= 14
Amare worked twice as many hours as Jing. Together, Amare and Jing worked a total of 42 hours. How many hours did each person work?
To solve this problem using a system of equations, we need to define our variables. Let's say the number of adults is 'A' and the number of students is 'S'.
From the given information, we can create two equations:
1) There were 10 more students than adults: S = A + 10
2) The total cost of the trip was $240: 18A + 12S = 240
We can now solve this system of equations using substitution.
Step 1: Substitute the value of S from equation 1 into equation 2:
18A + 12(A + 10) = 240
Step 2: Distribute multiplication:
18A + 12A + 120 = 240
Step 3: Combine like terms:
30A + 120 = 240
Step 4: Subtract 120 from both sides to isolate the variable:
30A = 240 - 120
30A = 120
Step 5: Divide both sides by 30 to solve for A:
A = 120 / 30
A = 4
So, there were 4 adults.
Step 6: Substitute the value of A back into equation 1 to find the number of students:
S = A + 10
S = 4 + 10
S = 14
Therefore, there were 4 adults and 14 students who went to see the play.
s = a+10
18a+12s = 240