At a Concert, tickets for adults cost $4.00 and tickets for students cost $2.50. How many of each kind...?

Question

At a Concert, tickets for adults cost $4.00 and tickets for students cost $2.50. How many of each kind of ticket were purchased if 125 tickets were bought for 413.00 dollars ? Im having a lot of problems knowing how to set uo the equation plez help. thanks.

Answer 1

it is a systems of equations. Set up two equations:

1. A + C = 125 (Adult ticktets plus Child tickets equal 125 tickets)
2. 4A + 2.5C = 413 (that's the total prices)

Solve equation 1 for one of the variables and substitute it into equation 2. Then you can solve for one variable. Once you have one, the other is easy.

Answer 2

this is the funnest kind of algebra

first you look at the question, it asks, how many of each kind of ticket, so the number of each kind of ticket is the variable

a=number of adult tickets
s=number of student tickets

now we look at what it tells us, first it says 125 tickets were bought
that means that the adult tickets plus the student tickets equals 125

first equation:s+a=125

then it tells us that it cost 413 bucks (we already know what each kind of ticket cost) so the next equation is:

a*4.00+s*2.50=413.00

obviously if a is the number of adult tickets and you multiply that times the cost of adult tickets you get the cost of all the adult tickets, and the same for the student tickets, add it together, you get the total cost

now it is just simultaneous equation solving

a+s=125
4a+2.5s=413

there are lots of ways to solve that, simple substitution is pretty easy here, solve the first equation for a, a=125-s, then substitue that for "a" in the next equation

4*(125-s)+2.5s=413
500-4s+2.5s=413
-1.5s=-87
s=58

and, if s=58, and a+s=125, then a=67

remember, make your unkonwns based on what the question wants you to find, then make your equations from what the problem states, then just solve and gloat

good luck
keep at it
math is power

Answer 3

Let x be the number of adult tickets and y be the number of student tickets

x costs $4 each and y cost $2.5 each and the total is $413

in terms of costs:
x * $4 + y * $2.5 = $413
or
4x + 2.5y = 413

in terms of number of tickets:
x + y = 125 or y = 125 - x

replace y in the first equation
4x + 2.5(125-x) = 413

then, do the rest for yourself.

Answer 4

let x=number of adult tickets sold
y= number of student ticket sold

then: x + y= 125 (1)

4(x) + 2.5(y)= 413 (2)

rearranging equation (1)

y= 125-x (1a)

Substitute equation (1a) to equation (2)

4x + 2.5(125-x)=413
4x + 312.5 - 2.5x=413
1.5x + 312.5 =413
1.5x = 413- 312.5
1,5x= 100.5
x= 67 tickets

substitute x=67 to equation (1)
x + y = 125
67 + y =125
y= 125-67
y= 58 tickets

67 adult tickets and 58 student tickets were sold.

Answer 5

if adults ticket=a and student's ticket=s , we have:
a+s=125
4a+2.5s=413
We will remove "a" by multiplying the first one by -4.
(-4)a+(-4)s=(-4)125
4a+2.5s=413
We will now add them together.
((-4a)+4a)+((-4s)+2.5s)=((-500)+413)....(it's a little confusing.)
Which gives us.
-1.5s=-87
by multiplying it by -1, we have
1.5s=87
s=87/1.5
s=58
let go back now...you remember a+s=125...let's plug 58 in "s".
a+58=125
a=125-58
a=67
....the adults bought 67 tickets and the students bought 58 tickets

Answer 6

assume there be 'n' newborn tickets bought. Then there might want to be '2n' scholars tickets bought. As there have been one hundred and ten tickets bought in all, no. of man or woman tickets bought equals to (one hundred and ten-(n+2n)) = one hundred and ten-3n. now one has following linear equation from the question documents, $(5*n)+ $(15*(one hundred and ten-3n))+$(10*2n) = $1250. therefore, $ (1650-20n) = $1250 20n=four hundred. n= 20. therefore entire man or woman tickets bought= one hundred and ten- 3*20 = 50.

Answer 7

4x + 2.5y = 413
x + y = 125

x + y = 125
y = -x + 125

4x + 2.5(-x + 125) = 413
4x - 2.5x + 312.5 = 413
1.5x + 312.5 = 413
1.5x = 100.5
x = 67

y = -67 + 125
y = 58

ANS :
67 Adult Tickets
58 Student Tickets

Answer 8

I'll set it up for you then you solve it.
a=adult; s=student
4A+2.5S=413 here we speak of dollars
A+S=125 here we speak of # of tickets
now multiply to simplify