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OleMash [197]
3 years ago
6

a total of 440 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student t

ickets sold was three times the number of adult tickets sold. How many adult tickets were sold.
Mathematics
1 answer:
diamong [38]3 years ago
5 0
Important:  represent your unknowns.  You might represent "number of adult tickets sold" by "a" and "number of student tickets sold" by "s."

How many tickets were sold, altogether?  Express this sum algebraically, using "a" and "s."

How does the number of student tickets sold compare with the number of adult tickets sold?  Express this algebraically in therms of "a" and "s."
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Answer:

See proof below

Step-by-step explanation:

Let r=\frac{w+z}{1+wz}. If w=-z, then r=0 and r is real. Suppose that w≠-z, that is, r≠0.

Remember this useful identity: if x is a complex number then x\bar{x}=|x|^2 where \bar{x} is the conjugate of x.

Now, using the properties of the conjugate (the conjugate of the sum(product) of two numbers is the sum(product) of the conjugates):

\frac{r}{\bar{r}}=\frac{w+z}{1+wz} \left(\frac{1+\bar{w}\bar{z}}{\bar{w}+\bar{z}}{\right)

=\frac{(w+z)(1+\bar{w}\bar{z})}{(1+wz)(\bar{w}+\bar{z})}=\frac{w+z+w\bar{w}\bar{z}+z\bar{z}\bar{w}}{\bar{w}+\bar{z}+\bar{w}wz+\bar{z}zw}=\frac{w+z+w+|w|^2\bar{z}+|z|^2\bar{w}}{\bar{w}+\bar{z}+|w|^2z+|z|^2w}=\frac{w+z+\bar{z}+\bar{w}}{\bar{w}+\bar{z}+z+w}=1

Thus \frac{r}{\bar{r}}=1. From this, r=\bar{r}. A complex number is real if and only if it is equal to its conjugate, therefore r is real.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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