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

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).