Question 1083064
We have two unknowns: the cost of one adult ticket, and the cost of one youth ticket


Since we have two unknowns, let's make
x = the cost of one adult ticket
y = the cost of one youth ticket
both costs are in dollars


The fact that "The youth ticket price is discounted 20% off the adult ticket price" implies


cost of youth ticket = (cost of adult ticket) - (20% of cost of adult ticket)
y = x - (20% of x)
y = 1x - 0.2x
y = (1 - 0.2)x
y = 0.8x
So whatever the adult ticket cost is, you take 80% of it to get the youth ticket cost.


We're also given "Total amount paid is $4642.00 for tickets for 5 adults and 1 youth", so this means,
5x+y = 4642.00

We can replace the 'y' with 0.8x since the two expressions are equal. We now have
5x+0.8x = 4642.00


Let's solve for x
5x+0.8x = 4642.00
5.8x = 4642.00
5.8x/5.8 = 4642.00/5.8
x = 800.344827586207
the last value above is approximate. Round this to the nearest penny to get 800.34


So the cost of one adult ticket is roughly $800.34


The cost of one youth ticket is y = 0.8*x = 0.8*800.34 = 640.272 which rounds to $640.27

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In summary,


One adult ticket costs $800.34 
One youth ticket costs $640.27


We can check the answer below
5x+y = 4642.00
5*800.34+640.27 = 4642.00
4001.7+640.27 = 4642.00
4641.97 = 4642.00


Note: due to rounding error, we're off by a few pennies (3 cents to be exact). So I recommend that you make sure you wrote down the proper values. I have a feeling there's a typo somewhere. If not, then it's possible that the rounding error occurred elsewhere.