what do i do. i dont understand

Question

on the first day of ticket sales the school sold 3 senior citizen and 9 children tickets for a total of 75. the school took in 67 on the second day by selling 8 senior citizens and 5 child tickets. what is the price on each of one senior citizen and one child ticket?

Answer 1

First, I recommend assigning a letter to both types of tickets:

s = senior citizen

c = child

Now we know both of the variables we're looking for :D

Next, make each separate statement into an equation:

3 senior citizen tickets (3s) and 9 children tickets (9c) sold for a total of $75 would be 3s+9c=75

8 senior citizen tickets (8s) and 5 children tickets (5c) sold for a total of $67 would be 8s+5c=67

Now with a little rearranging and substituting we can easily solve for the cost of a single ticket for both senior citizens and children!

The first equation:

3s+9c=75

~subtract 9c from both sides to isolate the s variable~

3s=75-9c

~divide by 3 to get the s variable completely alone~

s=25-3c

Then substitute this cool equation into the s variable in the second equation!

8s+5c=67

8(25-3c)+5c=67

~multiply it out~

200-24c+5c=67

~now solve for c woohoo~

200-19c=67

19c+67=200

19c=133

c=7

So, now we know that a children's ticket costs $7. Finally, we can plug this back into the first simplified equation and find the cost of a senior citizen's ticket!

s=25-3c

s=25-3(7)

s=25-21

s=4

There we go! A senior citizen's ticket costs $4. This method can be applied to various word problems in your future studies <3

Answer 2

3s+9c=75

8s+5c=67

you need to solve the above equations to get the answer

Answer 3

3s + 9c = 75

8s + 5c = 67

Solve for either s or c