Yolanda sold total 50 ticket. Adult ticket cost 5 dollar each. Student ticket cost 3 dollar each.she total collected 180 dollar. How many adult ticket did she collected? and how many student ticket did she collected?

Question

mathstudent55 · Answer

Let a = number of adult tickets.
Let s = number of student tickets.

She sold a total of 50 tickets.
Can you write an equation that shows the total number of adult and student tickets is 50 using variables a and s?

jamanorthi · Answer

A+s=50 is it like this

mathstudent55 · Answer

Great.
We have one equation: a + s = 50

Now we need a second equation. We will get it from the prices of the tickets and the total amount of money collected.

jamanorthi · Answer

A5+S3=180    then how do i solve those two equation

mathstudent55 · Answer

Each adult ticket costs $5, and a tickets were sold. How much money do a tickets at $5 each cost?
Then we do the same for student tickets. s number of student tickets were sold at $3 each. What is the cost of s tickets at $3 each?

jamanorthi · Answer

i am kind of confused now

mathstudent55 · Answer

Ok, you got it already.
We have this system of equations:

a + s = 50
5a + 3s = 180

Is there any method of solving a system of equations you prefer, substitution or addition?

mathstudent55 · Answer

Let's use substitution. It's a very common method of solving a system of equations.

jamanorthi · Answer

okay

jamanorthi · Answer

but now how do i solve these two equation

mathstudent55 · Answer

In substitution, first you solve one equation for one variable.
Then you substitute that into the other equation.

mathstudent55 · Answer

Let's solve the first equation for a.

a + s = 50

If we subtract s from both sides, we'll get a by itself. That's what we want.

mathstudent55 · Answer

a + s =       50
   -s      -s
----------------
a       = -s + 50

mathstudent55 · Answer

Now that we have a = -s + 50, we substitute that into the second equation. Where we see a in the second equation, we replace it with -s + 50.

5a + 3s = 180

5(-s + 50) + 3s = 180   <------ This is the substitution step.

jamanorthi · Answer

then how do i solve 5[-s+50]+3s=180

mathstudent55 · Answer

Now we have an equation with only one variable, s, so we can solve for s.

5(-s + 50) + 3s = 180

Distribute the 5:

-5s + 250 + 3s = 180

Combine -5s and 3s:

-2s + 250 = 180

Subtract 250 from both sides:

-2s = -70

Divide both sides by -2:

s = 35.

Now that we have s = 35, we substitute this value into the first original equation and solve for a:

a + s = 50
a + 35 = 50

Subtract 35 from both sides:

a = 15

We get a = 15 and s = 35.

Since this was a word problem, and we were asked a number of tickets for the adults and students, we answer with a statement:

She collected 15 adult tickets and 15 student tickets.

(We should not hand in an answer of a = 15 and s = 35 because the variables a and s were used by us to solve the problem, but they are not stated in the problem.)

jamanorthi · Answer

how did u distrute the 5 from 5[-s+50]+3s=180

jamanorthi · Answer

and why did u combined -5s and 3s

mathstudent55 · Answer

The distributive property is:

a(b + c) = ab + ac

We had 
5(-s + 50), 
so following the pattern of the distributive property above we get:

5(-s + 50) = (5) * (-s) + 5 * 50 = -5s + 250

Since that was part of an equation, the rest of the equation was still there:

5(-s + 50) + 3s = 180
-5s + 250 + 3s = 180

mathstudent55 · Answer

When you are solving an equation with one variable, you need to combine all terms that have that variable.

In our case, we had

-5s + 250 + 3s = 180

We need all terms with s combined on the left side, and all numbers on the right side, so that in the end we have only s on the left side equaling a number.

We combine terms with s:

-5s + 250 + 3s = 180
-5s + 3s + 250 = 180
-2s + 250 = 180

Then we subtract the number 250 to the right side, so we have only the terms with s on the left side and the numbers on the right side.

-2s = -70

Now we do have s on the left side, but it is still being multiplied by -2. We want s by itself, so we divide both sides by -2

s = 35

jamanorthi · Answer

i have one more question left why did u distribute?

jamanorthi · Answer

And thank u so much u really help me a lot.

mathstudent55 · Answer

You're welcome.

mathstudent55 · Answer

Since you can't combine unlike terms -s and 50, you need to distribute to get rid of the parentheses.