word problem

Question

The Jurassic Zoo charges
?$13
for each adult admission and
?$10
for each child. The total bill for the
250
people from a school trip was
?$2689.
How many adults and how many children went to the? zoo?

Answer 1

x=# of adults

250-x=# of children

13x+10(250-x)=2689

13x+2500-10x=2689

3x+2500=2689

3x=2689-2500

3x=189

x=189/3

x=63 adults

250-63=187 children

Answer 2

Let A = the number of adults in the 250 people

Let C = the number of children in the 250 people

Two equations connect these two variables:

A + C = 250

$13A + $10C = $2689

Substitiution seems best. Solve the first equation for A or C; I'll solve for C:

C = 250 - A, and sub the right side of that in place of C the second equation, using parentheses (dropping the $ for convenience):

 

13A + 10(250 - A) = 2689, multiply out and combine like terms:

13A + 2500 - 10A = 2689

3A = 2689 - 2500

3A = 189

A = 189/3

  = 63 adults

C = 250 - 63 = 187 children