Search 83,506 tutors
FIND TUTORS
Ask a question
0 0

275 tickets are sold. kids tickets cost $3 while adults cost $5. total value is $1,025. how many of each ticket is sold>

Tutors, please sign in to answer this question.

1 Answer

Step 1: Define your variables.
 
#of adult tickets = x
# of kids tickets = y
 
Step 2: What do you know?
 
The number of kids tickets added to the number of adult tickets is equal to the total number of tickets. This can be expressed as:
 
x + y = 275
 
Great! But that's not incredibly useful all by itself. What else do you know? The total money made (1025$) will be equal to the money made from adult tickets plus the money made from kids tickets.
 
(3$ * y) + (5$ * x) = 1,025$ ...........simplify
3y + 5x = 1025 
 
These equations each have two variables! To solve for  a variable, you need an equation with just one variable.
 
Step 3: Solve for x relative to y.
 
Starting with your simplest equation, determine the value of one of your variables. We'll find x.
 
x + y = 275
x = 275 - y
 
This allows us to combine our equations.
 
Step 4: Combine equations. 
 
Now you know what x is relative to y. You can plug this new value into your second equation.
 
3y + 5x = 1,025
3y + 5(275 - y) = 1,025
 
Step 5: Solve for y.
 
Your new and improved situation only has one variable. This means you can solve it.
 
3y + 5(275 - y) = 1,025 -------- distribute the 5
3y + 1375 - 5y = 1,025 --------- simplify the variable numbers    
-2y  + 1375 = 1,025 ------------ subtract the whole number
-2y = -350 ----------------------- divide by y
y = 175
 
Step 6: Solve for x.
 
Now that we know what y is, we can plug it back into the simple equation to find x.
 
x + y = 275
x + 175 = 275
x = 100
 
So now we have both variables. 
x = 100
y = 175
 
Recall what our variables represent, and you have your answer. There are 100 adult tickets, and 175 kids tickets sold.
 
This method of combining equations to solve one variable at a time is useful whenever you have multiple equations  with the same variables.