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If 104 people attend a concert and tickets for adults cost $2.25 while tickets for children cost $1.75
and total receipts for the concert was $202.5, how many of each went to the concert?
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Solution 1 (using one equation in one unknown)
Let x be the number of adult ticket bought.
Then the number of children tickets bought is (104-x).
The "value" equation is
225*x + 175(104-x) = 20250. (1)
Reduce by 25 all terms in both sides:
9x + 7*(104-x) = 810.
9x + 728 - 7x = 810,
2x = 810 - 728,
2x = 82 ---> x = = 41.
Answer. 41 adult tickets and 104-41 = 63 children tickets.
Solution 2 (using a system of two equations in two unknown)
Let "x" be the number of the adult ticket bought, and
let "y" be the number of the children ticket bought.
Then you have a system of two linear equations in two unknowns
x + y = 104, (1)
225x + 175y = 20250. (2) (this is the "value" equation in cents)
From the equation (1), express y = 104-x, and substitute this expression into the equation (2). You will get
225*x + 175(104-x) = 20250. (3)
The equation (3) is a single equation for the unknown "x".
It coincides with the equation (1) of the Solution 1 above.
Use the same procedure as in the Solution 1 to find "x".
Then find "y".
You will get the same answer, of course.