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Monica [59]
1 year ago
13

A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total

admission revenue, not including sales tax, and had a total of 450 guests. The system of equations below can be used to model the number of guests that were children, x, and the number of guests that were adults, y.
Mathematics
1 answer:
Natali [406]1 year ago
4 0

Answer:

There were 172 guests that were children and 278 guests that were adults

Step-by-step explanation:

Step 1: State what is known

It is $25 per adult

It is $12 per child

The made $9014 dollars

There were 450 guests

Step 2: Define equations

25y + 12x = 9014 -----1

x + y = 450 ------------2

Step 3: Rearrange equation 2 for x

x + y = 450

x = 450 - y --------------3

Step 4: Substitute 3 into 1 for y and solve for y

25y + 12(450 - y) = 9014

25y + 5400 - 12y = 9014

13y = 3614

y = 3614/13

y = 278

Step 5: Substitute y = 278 into 3 to solve for x

x = 450 - (278)

x = 172

Therefore 172 children and 278 adults visited the museum

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What is the equation of a line through the points (0, 9) and (3, 0)?
erastova [34]

Answer:

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Step-by-step explanation:

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Sarah’s stands on a ground and sights the top of a steep Clift at a 60 degree angle of elevation she then steps back 50 meters t
SashulF [63]

Answer:

Cliff is 45 m tall.

Step-by-step explanation:

Given:

Height of Sarah = 1.8 m

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As shown in the figure we have two right angled triangles SPQ and SPR.

Let the height of the cliff be h meters and h= h_1+h_s.

Using trigonometric ratios:

tan (Ф) = opposite/adjacent

In ΔSPQ.                                        In ΔSPR.

⇒ tan(60) = \frac{h_1}{x} ...equation (i)        ⇒ tan (30)=\frac{h_1}{x+50}  ...equation (ii)

Dividing equation (i) and (ii)

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⇒ 3 = \frac{x+50}{x}

⇒ 3x=x+50

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To find h_1 plugging x=25 in equation (i)

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⇒ h_1=25\times 1.73

⇒ h_1=43.25 meters

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⇒ h= h_1+h_s

⇒ h= 43.25+1.8

⇒ h=45.05 meters

The cliff is 45 m tall to the nearest meter.

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