a baseball game charges $3 for a ticket and $7 for adults. One game 400 tickets worth $1760 were sold, how many adults and how many children tickets were sold

Question

johnweldon1993 · Answer

Alright, so you know that in all....the sum of children and adult tickets sold is 400

so this can be written as

c + a = 400

We know that each child ticket is 3 and each adult is 7...so now we have an equation

3c + 7a = 1760

2 equations...2 unknowns...can you solve from here?

anonymous · Answer

no, i dont get any of it

anonymous · Answer

@johnweldon1993

johnweldon1993 · Answer

Alright we'll walk through it...

c + a = 400
3c + 7a = 1760

Do you see where I got those equations from?

anonymous · Answer

yea, the tickets sold and how much it came out too.

johnweldon1993 · Answer

Right...so this is called a "system of equations"

To solve it we can use a few methods...but the easiest here would be the substitution method..

What this method says to do...is solve one of these equations for a variable...then substitute that value into the other equation to solve for the other...

so here...

johnweldon1993 · Answer

c + a = 400
3c + 7a = 1760

Lets solve that top equation for the variable 'c' ...

How do we isolate 'c' in that equation? well we subtract 'a' from both sides.

c + a = 400
   - a      - a
------------
c = 400 - a

Still with me?

anonymous · Answer

yea.

johnweldon1993 · Answer

So now lets look at that second equation

3c + 7a = 1760

Well....we just solved and figured out that 'c' = 400 - a....so lets substitute that into this equation...so wherever you see a 'c' ...you replace it with (400 - a)

so

3c + 7a = 1760

would become

3(400 - a) + 7a = 1760

what do we do from here?

anonymous · Answer

400-400 then 400-1760?

johnweldon1993 · Answer

Not quite...so you would distribute the 3 into the parenthesis... so you multiply each term in the parenthesis by 3

3(400 - a) + 7a = 1760

3 times 400 is 1200
3 times -a = -3a

so now we have...

1200 - 3a + 7a = 1760

Now what?

anonymous · Answer

3a + 3a 7a+3a so it would be 1200+10a=1760

johnweldon1993 · Answer

Well remember it is -3a

so when we combine the like terms...

-3a + 7a is equal to 4a right? because -3 + 7 = 4

So now we have

1200 + 4a = 1760

Next up?

anonymous · Answer

1200-1200 1200-1760 so 4a=560 4a /4a 4a/560 so a=140

johnweldon1993 · Answer

Right!

So we have that 140 Adult tickets were sold.

Well, we know that there were 400 total sold...so how many children tickets were sold??

anonymous · Answer

260

johnweldon1993 · Answer

And there's your answer :) you can check it by plugging both numbers into the equations and solving

anonymous · Answer

ok, Thank you so much!(:

johnweldon1993 · Answer

Anytime :)

anonymous · Answer

(: