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lana [24]
3 years ago
6

Elisa school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 8 adult tickets and

3 children tickets for a total of $119. The school took in $135 on the second day by selling 10 tickets and 1 child ticket. What is the price each of one adult ticket and one child ticket?
Mathematics
1 answer:
Margarita [4]3 years ago
5 0

<u>ANSWER: </u>

Fare of adult tickets is $13 and fare of child tickets is $5.

<u>SOLUTION: </u>

Given, Elisa school is selling tickets to the annual talent show.  

Let, adult ticket fare be x and child ticket fare be y.

On the first day of ticket sales the school sold 8 adult tickets and 3 children tickets for a total of $119.

Then, 8x + 3y = 119 --- (1)

The school took in $135 on the second day by selling 10 adult tickets and 1 child ticket.  

Then, 10x + y = 135

y = 135 – 10x ---- (2)

Now, substitute y value in (1)

8x + 3(135 – 10x) = 119

8x + 3 × 135 – 3 × 10x = 119

8x + 405 – 30x = 119

405 – 119 = 30x – 8x

286 = 22x

x = \frac{268}{22}

x = 13

Now, substitute x value in (2)

y = 135 – 10(13)

y = 135 – 130  = 5

Hence, fare of adult tickets is $13 and fare of child tickets is $5.

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#1) 
A) b = 10.57
B) a = 22.66; the different methods are shown below.
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A) Let a = the side opposite the 15° angle; a = 1.35.
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A) We know that the sine ratio is opposite/hypotenuse.  The side opposite the 25° angle is b, and the hypotenuse is 25:
sin 25 = b/25

Multiply both sides by 25:
25*sin 25 = (b/25)*25
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B) The first way we can find a is using the Pythagorean theorem.  In Part A above, we found the length of b, the other leg of the triangle, and we know the measure of the hypotenuse:
a²+(10.57)² = 25²
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Subtract 111.7249 from both sides:
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Take the square root of both sides:
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The second way is using the cosine ratio, adjacent/hypotenuse.  Side a is adjacent to the 25° angle, and the hypotenuse is 25:
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Multiply both sides by 25:
25*cos 25 = (a/25)*25
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The third way is using the other angle.  First, find the measure of angle A by subtracting the other two angles from 180:
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Side a is opposite ∠A; opposite/hypotenuse is the sine ratio:
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Multiply both sides by 25:
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A) Let side a be the one across from the 15° angle.  This would make the 15° angle ∠A.  We will define b as the side marked 4 and c as the side marked 3.  We will use the law of cosines:
a² = b²+c²-2bc cos A
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a² = 25-24cos 15
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Take the square root of both sides:
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Use the law of sines to find m∠B:
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Cross multiply:
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Divide both sides by 1.35:
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(4*sin 15)/1.35 = sin B

Take the inverse sine of both sides:
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Subtract both known angles from 180 to find m∠C:
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Cross multiply:
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Divide both sides by sin 52:
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Use the law of sines to find side a:
sin C/c = sin A/a
sin 52/12 = sin 83/a

Cross multiply:
a*sin 52 = 12*sin 83

Divide both sides by sin 52:
(a*sin 52)/(sin 52) = (12*sin 83)/(sin 52)
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