Word problem help?

Question

A movie theater sells tickets for 8.00 each with Seniors receiving a discount of 3.00. One evening the theater sold 605 tickets and took in 3748 in revenue. How many of each type of tickets were sold?

Can't figure that one out.

Answer 1

If they sold 605 tickets at full price ($8) they would have made
$4840.

But they made $3748.

$4840 - $3748 = 1,092

Divide 1092 / 3 = 364 tickets sold at reduced prices and 241 at regular prices.

You can also do this with algebra:

Let S be the number of reduced price senior tickets.
Let T be the number of regular tickets.

S + T = 605
5S + 8T = 3748

Now solve for S:
S = 605 - T

Substitute into the second equation:
5(605 - T) + 8T = 3748

3025 - 5T + 8T = 3748

3T + 3025 = 3748
3T = 723
T = 723 / 3
T = 241

Then solve for S:
S = 605 - T
S = 605 - 241
S = 364

Either way the answer is:
241 tickets at full price
364 tickets at the senior price

Answer 2

Regular price = $8
Senior = $5
Let S = the number of senior tickets sold
The number of regular tickets sold is 605 - S

Revenue = 5 S + (605 - S) * 8 = 3748
5S + 4840 - 8S = 3748
-3S = -1092
S = 364
364 senior tickets and 241 regular priced tickets were sold.

Answer 3

OK

Full price tickets = 8 = a
Senior discount tickets =8-3=5 =b

a+b = 605
8a + 5b = 3748

Use substitution
a = 605-b

8(605-b) + 5b = 3748
4840 - 8b + 5b = 3748
-3b = -1092
b = 364

So there were 364 senior discount tickets sold.

605 - 364 = a ; a = 241

There were 241 full price tickets sold.

Proof

8(241) + 5(364) = 3748??
1928 + 1820 = 3748??
3748 = 3748 YES!!

Hop that helps.

Answer 4

I HATE math! But I LOVE the challange!

My guess is: 241 tickets @ $8.00
364 tickets @ $5.00

I have to tell you the reason that I said "My guess it:", is that I'm not sure how I arrived at this. I know there is a logical way and I don't know what it is....

For whatever reason, I did this:

605 tickets X $8.00 = $ 4,840
605 tickets X $5.00 = $ 3,025

$4,840 minus $3,025 = $1815

Total Revenue $ 3,748 minus $1,815 = $1,933
$1,933 divided by $8.00 ticket = 241

605 total tickets minus 241 tickets= 364 tickets

I would also like to know the correct way to arrive at the answer. I hope someone can show us.

Answer 5

r = # of regular tickets
s = + of senior tickets

the theater sold 605 tickets

1) r + s = 605
s = 605 - r

and took in 3748 in revenue

2) 8r + 5s = 3748

8r + 5(605 - r) = 3748 {substitute for s from eq 1}

8r + 3025 - 5r = 3748

3r = 723

r = 241

1) s = 605 - 241

s = 364

Check

8(241) + 5(364) = 3748

1928 + 1820 = 3748

3748 = 3748

Answer 6

solution:

let x = number of non senior , y = number of ticket for seniors

since Seniors receiving a discount of 3.00 = 8 - 3 = 5

x + y = 605 (eq1)

8x + 5y = 3748 (eq2)

from eq 1,

x = 605 - y (eq3)

substitute x in eq 2,

8x + 5y = 3748

8 ( 605 - y ) + 5y = 3748

4840 - 8y + 5y = 3748

combined like terms, the unknow must be in possitive form, we have

4840 - 3748 = 8y - 5y

1092= 3y

364 = y number of seniors.

solve fo x, used eq 1 or eq 3 to solve for x,

i used eq 3,

x = 605 - y

x = 605 - 364

x = 241 is the number of non seniors.

Answer 7

605*8 = 4840 <- what they would have made at full time

4840-3748 = 1092 <-different due to seniors

1092/3 = 364 <- total senior tickets sold

605-364 = 241 <- total regular tickets sold

proof:

241(8) + 364(5) = 3748

Answer 8

Let there be x seniors and y adults
x+y=605 -- (1)
5x+8y=3748 -- (2)
solve for x and y
from (1) y=605-x
Plug into (2)
5x+8(605-x)=3748
5x+4840-8x=3748
-3x=-1092
x=364 (seniors)
y=241 (using (1))

Answer 9

x - number of $8 tickets
y - number of $5 senior tickets

x + y = 605
8x + 5y = 3748

solve the two eqn:

x = 241, y = 364

Answer 10

8x + 5Y = 3748
x+y = 605

x = 605 - y

8(605-y)+5y=3748
4840-8y+5y=3748
4840-3y=3748
3y=4849-3738=1092
y=1092/3=364

x+364=605
x=241

241 adults and 364 seniors