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Museum passes cost $5 for adults and $2 for children. One day the museum sold 1820 passes for $6100. How many of each type were sold?

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2 Answers

X - number of children passes sold
 
1820 - X --- Number of  adults passes sold
 
   X ( $2) + ( 1820 - X ) $5 = $6100   ( 1)
 
      Solve for X , in equation ( 1)
 
 
    2X + 9100 - 5X = 6100
 
     -2X =  -9100 + 6100 = -3000
 
        X = 1500      / # of children passes sold
 
        1820 - 1500 = 320   / # of adult passes sold.
 
    Remember always choose a variable for unknown , what problem is asking to find.
 
 
 
The key to this problem is creating an equation to relate the things you know.
 
We know that 1820 passes were sold.
What we don't know yet is how many adult tickets were sold. So let's choose some variable x to represent that quantity.
That means that the remaining tickets, (1820-x), represents the number of children's tickets sold.
 
You know that the money made from the adult tickets is 5*(num adult tickets sold) and the money from children's tickets is 2*(num children's tickets sold). Moreover you know that the total amount of money made is $6100.
 
So in summary:
adult money + childrens money = total money
adult money = (# adult tickets sold) * 5
children's money = (# children's tickets sold) * 2
total money = 6100 
 
Without giving absolutely everything away, you now have a simple equation with one variable. Solve for x and you have your answer.