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Minchanka [31]
3 years ago
10

Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for

opening night totaled $2071.50. The equation 10.50a + 3.75b = 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?
adult tickets
Mathematics
2 answers:
bekas [8.4K]3 years ago
4 0
168 adult tickets were sold
vekshin13 years ago
4 0

Answer: There are 168 adult tickets that were sold.

Step-by-step explanation:

Let the number of adult tickets were sold be 'a'.

Let the number of student tickets were sold be 'b'.

Since we have given that

The ticket sales for opening night totaled as

10.50a+3.75b=2071.50

And the number of students attended  = 82

so, b = 82

So, we will put the value of b in the above equation:

10.50a+3.75\times 82=2071.50\\\\10.50a+307.5=2071.50\\\\0.50a=2071.50-307.5\\\\10.50a=1764\\\\a=\dfrac{1764}{10.50}\\\\a=168

Hence, there are 168 adult tickets that were sold.

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Answer: - 8.89%

I am going to explain you in detail ir order to help you to be able to do this kind of problems by yourself.

The definition of percent change, %, is:

          change
% = ---------------- * 100
        base value

The base value is from where you start or the value for which you want to asses the variation.

So, in this case the base value is 90 (starting value).

The change is final value - initial value = 82 - 90 = - 8. The negative sign means that the value decreased.

So, following the formula you get:

         82 - 90                - 8
% =  ----------- * 100 = -------- * 100 = - 8.89
            90                     90

Answer: the percent of change is - 8.89 %, meaning that the value decreased 8.89%.
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A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.

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