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Question 7698: Write a system of two equations in two unknown numbers for each problem. Solve each system by substitution.
Ticket Sales. Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?
Answer by drglass(89)   (Show Source):
You can put this solution on YOUR website! To solve a word problem, we have to translate from words to math. We are given four facts in words:
1) the price of an adult ticket is $3
2) the price of a student ticket is $2
3) the total receipts is $824, that is the amount of money spent on adult tickets and the amount of money spent on student tickets adds up to $824
4) twice as many adult tickets as student tickets were sold, in other words, the number of adult tickets sold is two times the number of student tickets sold.
Now, let's translate this to math. Start by giving names to things:
Well call "the number of student tickets sold" s
and "the number of adult tickets sold" a.
The value of the adult tickts sold $3a and the value of the student tickets sold $2s. The total amount spent on tickets is the sum of the value of the adult tickets sold and the student tickets sold. We are told that the total amount is $824. Mathematically, we write this statement as follows:
$3a + $2s = $824
Next we are total that the number of adult tickets a sold is two times the number of student tickets sold or 2s, this translates to:
a = 2s.
We now have two equations and two unknowns:(notice that I dropped the $ symbol, it is not important for the mathematics).
1) 3a + 2s = 824
2) a = 2s
Well, we can substitute a = 2s into 3a + 2s = 824 as follows:
3(2s) + 2s = 824, or
6s + 2s = 824,
8s = 824, dividing both sides by 8 we get
s = 103
We can use this value for s in the second equation to get:
a = 2(103) = 206
Now, let's translate this back, a means the number of adult tickets and s means the number of student tickets so, they sold 103 student tickets and 206 adult tickets.
Let's check this work. 103 student tickets are worth $2*103 = $206 and 206 adult tickets are worth $3*206 = $618. The total amount spent on tickets is the sum of the value of all the adult tickets and all the student tickets, which is  .
If we
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