Question

In 2016, Dell Museum in St. Petersburg, Florida offered individual, dual, and family memberships, which can cost $60, $60, and $100, respectively. Suppose in one month the museum sells a total of 81 new memberships, for a total of $6420. The number of dual memberships purchased is twice that of individual memberships. Write and solve a system of equations to determine the number of new individual memberships, dual memberships, and family memberships.

Answer 1

Let's use the information given to write a system of equations.

Let's represent the number of individual memberships as "x", the number of dual memberships as "y", and the number of family memberships as "z".

From the given information, we can write the following equations:

Equation 1: x + y + z = 81 (The total number of memberships sold is 81)
Equation 2: 60x + 60y + 100z = 6420 (The total cost of the memberships sold is $6420)

Now we can solve this system of equations to find the values of x, y, and z.

Answer 2

New individual memberships = 14

Dual memberships = 28

Family memberships = 39

Explanation:

Definition:

System of equations: A set of two or more equations that share the same variables.

Answer:

Let's use the following variables to represent the number of individual, dual, and family memberships sold:

• I = number of individual memberships
• D = number of dual memberships
• F = number of family memberships

We are given the following information:

The total number of new memberships sold is 81:

• I + D + F = 81

The total cost of the new memberships is $6420:

• 60I + 60D + 100F = 6420

The number of dual memberships purchased is twice that of individual memberships:

• D = 2I

We can now write the following system of equations:

• I + D + F = 81
• 60I + 60D + 100F = 6420
• D = 2I

We can solve this system of equations using substitution. Since we already have an expression for D in terms of I, we can substitute it into the first two equations. This gives us the following system of equations:

I + 2I + F = 81

60I + 60(2I) + 100F = 6420

Combining like terms, we get the following system of equations:

3I + F = 81

180I + 100F = 6420

We can now solve this system of equations using elimination.

Multiplying the first equation by -100, we get:

-300I - 100F = -8100

180I + 100F = 6420

Adding the two equations, we get:

-120I = -1700

Dividing both sides by -120, we get:

`\sf (-120I)/(-120) =( -1700)/(-120)`

I = 14

Now that we know the value of I, we can substitute it into the equation D = 2I to find the value of D:

D = 2(14) = 28

Finally, we can substitute the values of I and D into the equation I + D + F = 81 to find the value of F:

14 + 28 + F = 81

42 + F = 81

F = 81 - 42

F = 39

Therefore, the number of new individual memberships, dual memberships, and family memberships sold are 14, 28, and 39, respectively.