SOLUTION: I am not a student, but I need to solve a problem related to the cost of an activity; sadly, my receipt does not break down the cost per person. Total amount paid is $4642.00 for

Question 1083064: I am not a student, but I need to solve a problem related to the cost of an activity; sadly, my receipt does not break down the cost per person. Total amount paid is $4642.00 for tickets for 5 adults and 1 youth. The youth ticket price is discounted 20% off the adult ticket price.
I think the problem is:
5x + (x - 20%) = 4642
However, it has been approximately 35 years since I have done algebra and I do not remember how to handle the x - 20% portion of equation. I need to find the price of an adult for this activity. I'm not completely sure if this is a one variable equation or 2... HELP!
Thanks!
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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
--------------------------------------------------
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.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
given:
Total amount paid is $
tickets for adults and youth :
let's tickets for adults be and for youth
since youth ticket price is discounted %= off the adult ticket price, we know that

so

ticket for adults cost
-> discount of %
->cost of the ticket for youth
check:

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