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k0ka [10]
3 years ago
10

The very busy Freshman class is selling tickets for an upcoming field hockey game. The class sells 20 more student tickets than

adult tickets. The adult tickets cost $4 and the student tickets cost $2. The class made a total of $280 from ticket sales. How many of each type of ticket did they sell? Elaborate and clarify your reasoning.
1a. Define the variables in this system
b. Create equations to describe the relationships in this system between the variables
Mathematics
1 answer:
mixer [17]3 years ago
7 0

Answer:

60 student tickets and 40 adult tickets were sold

Step-by-step explanation:

Let s represent student tickets and a adult tickets, then the system of equations can be written as

s - a = 20 →(1)

2s + 4a = 280 → (2)

Multiply (1) by 4 and add to (2) to eliminate a

4s - 4a = 80 → (3)

Add (2) and (3) term by term

6s = 360 ( divide both sides by 6 )

s = 60

Substitute s = 60 into (1)

60 - a = 20 ( subtract 60 from both sides )

- a = - 40 ( multiply both sides by - 1 )

a = 40

Thus

60 student and 40 adult tickets were sold.

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Read 2 more answers
This question is down below. The picture attached below. <br> Thanks.
Ostrovityanka [42]

The vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

Given an equation showing profits of A Christmas vendor as

P=-0.1g^{2}+30g-1200.

We have to find the number of gingerbread houses that the vendor needs to sell in order to earn profit of $665.60 and $1500.

To find the number of gingerbread houses we have to put P=665.60 in the equation given which shows the profit earned by vendor.

665.60=-0.1g^{2}+30g-1200

0.1g^{2}-30g+1200+665.60=0

0.1g^{2}-30g+1865.60=0

Divide the above equation by 0.1.

g^{2}-300g+18656=0

Solving for g we get,

g=[300±\sqrt{(300)^{2}-4*1*18656 }]/2*1

g=[300±\sqrt{90000-74624}]/2

g=[300±\sqrt{15376}]/2

g=(300±124)/2

g=(300+124)/2       , g=(300-124)/2

g=424/2,  g=176/2

g=212,88

Because 212 is much greater than 88 so vendor prefers to choose selling of 88 gingerbread houses.

Put the value of P=1500 in equation P=-0.1g^{2}+30g-1200.

-0.1g^{2}+30g-1200=1500

0.1g^{2}-30g+1500+1200=0

0.1g^{2}-30g+2700=0

Dividing equation by 0.1.

g^{2}-300g+27000=0

Solving the equation for finding value of g.

g=[300±\sqrt{300^{2} -4*1*27000}]/2*1

=[300±\sqrt{90000-108000}] /2

=[300±\sqrt{-18000}]/2

Because \sqrt{-18000} comes out with an imaginary number so it cannot be solved for the number of gingerbread houses.

Hence the vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

Learn more about equation at brainly.com/question/2972832

#SPJ1

7 0
1 year ago
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