A teacher buys 50 train tickets for a school trip for a total cost of $1,200. She buys x number of student tickets for $20 each. She also buys y number of adult tickets for $30 each.
I sense a question in there somewhere...
x+y=50
20x+30y=1200
so, ...
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To find the number of student tickets (x) and adult tickets (y), we can set up a system of equations based on the information given.
Let's assume:
x = number of student tickets
y = number of adult tickets
Now let's write the equations:
1. The teacher buys 50 train tickets in total:
x + y = 50
2. The total cost of the tickets is $1,200:
20x + 30y = 1200
We now have a system of equations:
x + y = 50
20x + 30y = 1200
To solve this system, we can use the method of substitution.
Step 1: Solve the first equation for x.
x = 50 - y
Step 2: Substitute the expression for x in the second equation.
20(50 - y) + 30y = 1200
Step 3: Distribute and simplify.
1000 - 20y + 30y = 1200
10y = 200
y = 20
Step 4: Substitute the value of y back into the first equation to find x.
x + 20 = 50
x = 50 - 20
x = 30
So, the teacher buys 30 student tickets (x) and 20 adult tickets (y).