There were 305 tickets sold for a basketball game. The activity cardholders' tickets cost $1.25 and the non-cardholders' tickets cost $2.50. The total amount of money collected was $578.75. How many of each kind of ticket were sold?

## How many of each kind of ticket were sold?

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# 6 Answers

Let x = number of activity cardholder's tickets sold

Let y = number of non-activity cardholder's tickets sold

We know that x + y = 305 Eq. (1)

We also know that ($1.25)*x + ($2.50)*y = $578.75 Eq. (2)

Solve Eq. 1 for y and substitute into Eq. 2:

y = 305 - x and ($1.25)x + ($2.50)(305 - x) = $578.75

($1.25)x + $762.5 - ($2.50)x = $578.75

(-$1.25)x = $578.75 - $762.5

**x = 147 tickets**

Therefore,

**y = 158 tickets**Check

Does ($1.25)*(147) + ($2.50)(158) = $578.75? Yes!!!

You can solve this by using two equations, each with two unknowns, or variables.

The variables are the number of cardholders tickets (C), and the number of non-cardholders tickets (N).

There were 305 tickets sold, so the total of cardholders plus noncardholders is 305:

N + C = 305

Each cardholders ticket costs 1.25, so the amount from sales of cardholders tickets is 1.25 * C.

Each non-cardholders ticket costs 2.50, so the amount from sales of non-cardholders tickets is 2.50 * N.

The total sales is 578.75:

1.25C + 2.5N = 578.75

You now have two equations in two unknowns. Now, change the first equation to express one of the variables in term of the other (by subtracting C from both sides of the equation:

N + C = 305

N = 305 - C

Now, use substitution to eliminate N from the second equation:

1.25C + 2.5N = 578.75

substitute for N:

1.25C + 2.5(305 - C) = 578.75

distributive property:

1.25C + (2.5 * 305 - 2.5 * C) = 578.75

perform multiplication inside the parentheses

1.25C + (762.5 - 2.5C) = 578.75

eliminate the parentheses

1.25C - 2.5C + 762.5 = 578.75

combine variable terms

-1.25C + 762.5 = 578.75

subtract 762.5 from both sides of the equation

-1.25C = -183.75

divide both sides by -1.25

C = 147

Now that you know how many cardholder tickets were sold, use the original equation to determine the non-cardholder tickets:

N + C = 305

substitute for C:

N + 147= 305

subtract 147 from both sides of the equation:

N = 305 - 147

N = 158

C = 147, N = 158

There were 147 cardholder tickets sold, and 158 non-cardholder tickets sold. Double check by plugging those values into the second equation:

1.25C + 2.5N = 578.75

1.25 * 147 + 2.5 * 158 = 578.75

183.75 + 395 = 578.75

578.75 = 578.75

Kevin,

If we let x=number of activity cardholders and y= the number on non-activity cardholders the we were told that:

x+y=305 total number of tickets sold

and:

1.25x+2.5y=578.75 total revenue from ticket sales. This gives 2 equations with 2 unknowns x and y.

If you now multiply both sides of the first equation by 1.25 and subtract it from the second equation we have

1.25y=197.50, or y=158 and since x+y=305 x must be 147

The sales from activity cardholders =1.25*147 = 183.75

The sales from non act.cardholders=2.5*158 = 395 which totals to $578.75

Regards

Jim

Hi Kevin;

x=quantity of cardholders' tickets

$1.25x+$2.50(305-x)=$578.75

$1.25x+($762.50-$2.50x)=$578.75

$762.50-$1.25x=$578.75

Let's subtract $762.50 from both sides as we proceed to isolate x...

-$762.50+$762.50-$1.25x=$578.75-$762.50

-$1.25x=-183.75

Let's divide both sides by -$1.25 as we proceed to isolate x...

(-$1.25x)/-$1.25=(-$183.75)/(-$1.25)

x=147 cardholders' tickets

305-147=158 non-cardholders' tickets

Let's check our work...

[147($1.25)]+[158($2.50)]=$578.75

$183.75+$395.00=$578.75

$578.75=$578.75

Please note that I always indicate all information of cents as well as dollars for each monetary figure. Consistency is very important, and all initial figures of $1.25, $2.50 and $578.75 include such information. Therefore, all supplemental information
must include such too, even if it is 00 cents.

Let C be the number of cardholders.

1.25C + 2.5(305 - C) = 578.75

1.25C + 762.5 - 2.5C = 578.75

-1.25C = 578.75 - 762.5

-1.25C = -183.75

C = 147

**Cardholders 147, Non Cardholders 158**

x=cardholder ticket

y=non cardholder ticket

Do a system of equations:

x+y=305

1.25x+2.50y=578.75

Now multiply the top equation to get rid of one of the variables in order to solve the other:

-1.25x-1.25y=-381.25

1.25x+2.50y=578.75

This leads to:

1.25y=197.5 -> y=1197.5/1.25=158

Plug the y-value back into x+y=305 ->x+158=305 -> x=147

So there were 147 cardholder and 158 non-cardholder tickets sold

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