Answer:
42 Mega Million Tickets and 18 Scratch Off Tickets
Explanation:
We have two unknowns, the two numbers of tickets.
We need to define two variables and write two equations.
Let the number of Mega Million tickets = m.
Let the number of Scratch Off tickets = s.
A Mega Million ticket costs $5, so m tickets cost 5m.
A Scratch Off ticket costs $2, so s tickets cost 2s.
The cost of the tickets is: 5m + 2s. It is also $246.
That gives us the first equation which deals with the value of the tickets.
5m + 2s = 246
They bought m tickets plus s tickets, so the total number tickets that was bought is m + s. We are told that altogether 60 tickets were bought.
That gives us the second equation which deals with the number of tickets that were bought.
m + s = 60
We now have a system of equations.
5m + 2s = 246
m + s = 60
We will use the substitution method to solve the system of equations. We solve the second equation for m.
m = 60 - s
Now we substitute m in the first equation with 60 - s.
5m + 2s = 246
5(60 - s) + 2s = 246
We now have one equation in one unknown, so we can solve it for s.
300 - 5s + 2s = 246
-3s = -54
s = 18
Now we substitute 18 for s in the second original equation and solve for m.
m + s = 60
m + 18 = 60
m = 42
Answer: 42 Mega Million Tickets and 18 Scratch Off Tickets