Question 1200436: there were 16 000 people at a hockey game. for tickets some paid $10 & other paid $4. The total of receipts were $100 000. How many of each were sold?
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 10x + 4y = = 100,000
x + y = 16,000
from the second equation, y = 16,000 - x.
in the first equation, replace y with that to get 10x + 4 * (16000 - x) = 100,000
simlify to get 10x + 64000 - 4x = 100,000
combine like terms to get 6x + 64000 = 100,000
subtract 64000 from both sides of the equation and then divide both sides of the equation by 6 to get x = 36000 / 6 = 6000
this makes y = 16,000 = 6,000 = 10,000
you get x = 6,000 and y = 10,000
10x + 4y = 60,000 + 40,000 = 100,000 and you get x + y = 16,000, confirming the values of x and y are good.
your solution is that 6,000 ten dollar tickets and 10,000 four dollar tickets were sold.
Answer by ikleyn(52884)  (Show Source):
You can put this solution on YOUR website! .
there were 16 000 people at a hockey game. for tickets
some paid $10 & other paid $4. The total of receipts were $100 000.
How many of each were sold?
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Let x be the number of tickets at $10;
then the number of tickets at $4 is 16000-x.
The total money equation is
10x + 4*(16000-x) = 100000 dollars.
Simplify and find x
10x + 64000 - 4x = 100000
10x - 4x = 100000 - 64000
6x = 36000
x = 36000/6 = 6000.
ANSWER. 6000 tickets at $10, and the rest, 16000-6000 = 10000 tickets at $4.
CHECK. 6000*10 + 10000*4 = 60000 + 40000 = 100000 dollars, total. ! correct !
Solved.
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Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
Here is a quick and easy way to solve this kind of 2-part mixture problem without formal algebra (if, of course, a formal algebraic solution is not required).
If all 16,000 tickets had been $10 each, the total receipts would have been $160,000; if all had been $4 each, the total would have been $64,000.
Look at the three total prices (on a number line, if it helps) and observe/calculate that $100,000 is $36,000/$96,000 = 36/96 = 3/8 of the way from $64,000 to $160,000. That means 3/8 of the tickets were the more expensive ones.
ANSWER: 3/8 of 16,000, or 6000 of the tickets were $10 each; the other 10,000 tickets were $4 each.
CHECK: 6000(10)+10000(4) = 60,00+40,000 = 100,000
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