Question 1050974
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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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<U>Solution 1</U>  (using one equation in one unknown)


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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 = {{{82/2}}} = 41.

<U>Answer</U>.  41 adult tickets and 104-41 = 63 children tickets.
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<U>Solution 2</U>  (using a system of two equations in two unknown)


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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 <U>Solution 1</U> above.
Use the same procedure as in the <U>Solution 1</U> to find "x".
Then find "y".

You will get the same answer, of course.
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