algebra help pleez don't answer if u don't have the answer..?

Question

Suppose you are collecting the tickets for the school play. You collect 595 tickets. Admission is $5 for adults and $3 for students. The total amount of the money from ticket sales is $1951. You want to figure out how many adult tickets were sold.

a. Write a system of equations, letting a represent the number of adult tickets and a s represent the number of student tickets.

b. use the system to determine how many adult tickets were sold.

c. solve the system of equations by a different method.
d. do you get the same solution with each method? why or why not?

Answer 1

You can solve this equation several ways, and get the same answer. Here, I solved it using substitution.

First, assign your variables.

a=adult tickets
s=student tickets

You need to solve for the price as well as how many tickets. So, you create a system of equations.

5a + 3s = 1951 (This is the price) Equation 1
a + s = 595 (This is for the amount of tickets) Equation 2

Next you solve for one of the equations. Here, I'll solve for equation 2.

a = 595 - s

Next you substitute this for equation 1.

5 (595 - s) + 3s = 1951
2975 - 5s + 3s = 1951
2975 - 2s = 1951 - 2975

-2s = -1024
-2s/-2 = -1024/-2
s=512

Now, substitute this for a = 595 - s

a = 595 - s
a = 595 - 512
a = 83

There were 83 adult tickets, and 512 student tickets sold. Just substitute the values into the system of equations, and it will work. Hope this helps!

Answer 2

First you need to determine what you know:

(a) + (s) = 595 (the adult tickets plus the student tickets= 595)
now isolate the adult variable:
(a) = 595-(s)
now that you have solved an equation for the amount of tickets purchased by adults, look at the rest of the problem.
You know that:
5(a) + 3(s) = 1951 ($5 times every adult ticket plus $3 times every student tickets = $1951
so, now take your first equation were you solved for the number or adult tickets: (a) =595-(s)... your next step would be to replace the (a) variable in the second equation:
5(595-s) + 3(s) = 1951
simplify:
2975 - 5s +3s = 1951
2975-2s=1951
notice that your variable has a negative integer associated with it so make it positive by adding it to the other side of the equation:
2975=1951 + 2s
continue to simplify:
2975-1951= 2s
1024= 2s
1024/2=s
512=s
so now look at your original equation:
a + s = 595
substitute your calculated value for s:
a + (512)=595
simplify:
a=595-512
a=83
Now check your answer, using the second equation:
5 (83) + 3 (512) = 1951
415 + 1536 = 1951
1951=1951
So, 512 students purchased tickets at $3, and 83 teachers purchased tickets at $5.

Cheers,
ALK

Answer 3

a = number of adult tickets
s = number of student tickets
so a+s = 595...eqn 1
also 5a+3s = 1951..eqn 2
feom eqn 1 subtracting a from both the sides
s = 595-a ..eqn 3
substitute eqn 3 in eqn 2
5a+3(595-a) = 1951
5a+1785-3a = 1951
2a+1785 = 1951
subtracting 1785 from both the sides
2a = 166
so a = 166/2 = 83
substituting for a in eqn 3
s= 595-83 = 512

Different Method:
Mutiply eqn 1 by 3
3(a+s) = 3*595 = 1785
3a+3s = 1785 ..eqn 4
subtract eqn 4 from eqn 2
2a = 166
a =166/2 =88
remaining part as in the previous method

with both the methods you will get the same solution as you have valued the equalities in the same manner

Answer 4

This should work as well. Assume all tickets were sold to students. But this comes out to only $1785, leaving a difference of $166, which must have been spent by adults. As the ticket-price difference is $2, 166/2 = 83 adults. By subtraction you get 512 students.

Or if you do it the other way around, assuming all tickets were sold to adults, you should have $2975, a deficit of $1024. 1024/2 = 512 students.

Answer 5

a. Use the number of tickets sold to make the first equation: a+s=???.

Use the price of the tickets to figure out the second equation.

b. and c. You can do it!

d. Without even attempting to sove the problem, you should know that all methods will yield the same solution. If they didn't, one of them would be wrong.

Answer 6

Hmmm... That should be an easy one.

a + s = 595
5a + 3s = 1951
a = 595 - s and you should be able to do the rest.