PLEASE, Help ASP

Mathematics

1 answer:

Leokris [45]3 years ago

3 0

Answer:

39 child tickets

Step-by-step explanation:

Let x represent the number of child tickets sold,

let y represent the number of adult tickest sold.

"three times as many adult tickets as child tickets were sold," becomes

x = y/3 x is one-third the value of y

"$5.80 and adult admission is $9.20" and " for a total sales of $1,302.60" become

$5.80x + $9.20y = $1,302.60

We know that x = y/3, so substitute that into the second equation...

$5.80(y/3) + $9.20y = $1,302.60

Now solve for y...

$5.80y + $27.60y = $3,907.80 (multiply by 3 to get rid of the fraction)

$33.40y = $3,907.80 (combine like terms)

y = $3,907.80/$33.40 (divide both sides by $33.40 to isolate y)

y = 117

If there were 117 adult ticket sold, then there were

x = 117/3 child tickets

x = 39 child tickets

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Solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not

4vir4ik [10]

Answer:

x = 4 (extraneous solution)

Step-by-step explanation:

$\frac { 4 } { x - 4 } = \frac { x } { x - 4 } - \frac { 4 } { 3 } \\ \frac { 4 } { x - 4 } - \frac { x } { x - 4 } = - \frac { 4 } { 3 } \\ \frac { 4 - x } { x - 4 } = - \frac { 4 } { 3 } \\ 3 ( 4 - x ) = - 4 ( x - 4 ) \\ 1 2 - 3 x = - 4 x + 1 6 \\ 4 x - 3 x = 1 6 - 1 2 \\ x = 4 \\$

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back $x=4$ , we will get two fractions with zero denominator which would be undefined.