Admission to a local aquarium is $10 for adults and $7 for children. The aquarium collected $6,459 from the sale of 783 tickets. How many children's tickets were sold?

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Answer 1 · 2016-12-12T13:23:29

There were 457 children tickets sold.

First, let's define our variables:

We can call the number of tickets for adults #a#

We can call the number of tickets for children #c#.

Now we can right two equations which we can then solve using substitution:

#a + c = 783#

#10a + 7c = 6459#

Step 1) Solve the first equation for #a#:

#a + c - c = 783 - c#

#a = 783 - c#

Step 2) Substitute #783 - c# for #a# in the second equation and solve for #c#:

#10(783 - c) + 7c = 6459#

#7830 - 10c + 7c = 6459#

#7830 - 3c = 6459#

#7830 - 7830 - 3c = 6459 - 7830#

#0 - 3c = -1371#

#-3c = -1371#

#(-3c)/(-3) = (-1371)/(-3)#

#c = 457#

Step 3) Substitute #457# for #c# for the solution to the equation in Step 1) and calculate #a#:

#a = 783 - 457#

#a = 326#