The entire company went in together to buy lottery tickets. Inside the safe are two different types of lottery tickets. The Mega Million Tickets cost $5 each and the Scratch Off Tickets cost $2 each. They bought 60 tickets totaling $246. How many of each lottery ticket did the company purchase? Write and solve a system to represent a situation.

42 Mega Million Tickets and 18 Scratch Off Tickets

Step-by-step 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

42 Mega Million Tickets and 18 Scratch Off Tickets