Answer:
Let x = # of adult tickets sold (at $4.00 each)
Let y = # of child tickets sold (at $2.00 each)
We can take the above information, along with the 2000 tickets sold and the $6,400 collected, to get the following two math statements:
x + y = 2000 (Total unknown number of $4.00 + total unknown number of $2.00 tickets, equals a total of 2,000 tickets sold
4x + 2y = 6400 ($4.00 * unknown number of $4.00 tickets + $2.00 * unknown number of $2.00 tickets, equals the total of $6,400 collected in ticket sales
So, write these as:
x + y = 2000
4x + 2y = 6400
Take the first equation: Turn it into a y= statement, by subtracting 'x' from both sides, to get:
y = 2000 - x
Next, go to the 2nd equation. Where you see the 'y', substitute the y-value in its place: '2000 - x'
This gives you:
4x + 2 (2000 - x) = 6400
This then gives us: 4x + 4000 -2x = 6400
Collect like terms to get:
2x + 4000 = 6400
Subtract 4000 from both sides to get:
2x = 2400
Next, divide both sides by 2, to get x = 1200
We now know that there were 1,200 adult ($4.00) tickets sold; put this information back into the original equation:
1200 + y = 2000
Next, subtract 1200 from both sides, so that we can solve for y; which is:
y = 800
Next, check our work, by substituting back into the two original equations:
1200 + 800 = 2000 [Check]
4 * 1200 + 2 * 800 = 4800 + 1600 + 6400 [Check]
So: 1,200 tickets sold at $4.00 each; and 800 tickets sold at $2.00 each, final and correct answer.
Explanation: