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Rudik [331]
3 years ago
10

When the​ women's soccer team won the state​ championship, the parent boosters welcomed the team back to school with a balloon b

ouquet for each of the 18 players. The parents spent a total of ​$161.28 ​(excluding tax) on foil balloons that cost ​$1.96 each and latex​ school-color balloons that cost ​$0.14 each. Each player received 12 ​balloons, and all the balloon bouquets were identical. How many of each type of balloon did each bouquet​ include?
Mathematics
1 answer:
Ray Of Light [21]3 years ago
7 0

Answer:

Each bouquet included 8 latex balloons and 4 foil balloons

Step-by-step explanation:

Hi there!

Let x be the number of latex balloons and y the number of foil balloons. The total cost of the balloons will be the cost of each latex balloon times the amount (x) added to the cost of each foil balloon times the amount of these balloons (y). Then:

Cost of each latex balloon = 0.14

Amount of latex balloon = x

Cost of each foil balloon = 1.96

Amount of foil balloons = y

0.14 x + 1.96 y = 161.28

We also know that each player received 12 balloons. Since there are 18 players, the number of foil and latex balloons will be 18 · 12 = 216 balloons.

Then:

x + y = 216

So we have a system of equations that we can solve because we have two equations and two unknowns. Let´s solve it!

0.14 x + 1.96 y = 161.28

x + y = 216

Let´s solve the second equation for y:

x + y = 216

y = 216 - x

Now, let´s replace y in the first equation and solve it for x:

0.14 x + 1.96 y = 161.28

0.14 x + 1.96 (216 - x) = 161.28

Apply distributive property:

0.14 x + 423.36 - 1.96 x = 161.28

-1.82 x + 423.36 = 161.28

-1.82 x = 161.28 - 423.36

-1.82 x = -262.08

x = -262.08 / -1.82

x = 144

There are 144 latex balloons

Then:

y = 216 -144 = 72

There are 72 foil balloons

If 144 latex balloons are distributed among the 18 players, each player will receive (144/18) 8 balloons.

In the same way, if the 72 foil balloons are distributed among the players, each will receive (72/ 18) 4 balloons.

Then, each bouquet included 8 latex balloons and 4 foil balloons.

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Answer:

x=-2/k

Step-by-step explanation:

To solve you need to make x on one side while the other variables or numbers on the other.

First, you need to move the 9 to the other side by subtracting 9 from both sides: kx+9-9=7-9

Simplify: kx=-2

Now you need to divide by k into both sides in order to eliminate the k on kx:

x=-2/k

Answer: x=-2/k

Hope this helps!

3 0
2 years ago
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Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points. R
Mrac [35]

Answer:

Midpoint (-2,4)

distance nearest tenth = 8.9

The approximate distance = 9

Step-by-step explanation:

Formulas

PQ midpoint = (x2 + x1)/2, (y2 + y1)/2

distance d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )

Givens

x2 = -4

x1 = 0

y2 = 1

y1 = 7

Solution

M(PQ) = (-4+0)/2, (1 + 7)/2

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The midpoint is -2,4

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The distance = sqrt(16 + 64)

The distance = sqrt(80)

The distance = 4√5           exactly

The distance = 8.94    

The distance = 8.9            To the nearest tenth

Question 2

The distance is rounded to the nearest whole number which is 9.

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3 years ago
A portion of a roller coaster track is shown in the figure above. the roller coaster track is shown at ground level at point S a
eimsori [14]

Answer:

Step-by-step explanation:

This is classic right triangle trig.  The height of the hill is 78.4 which serves as the side opposite the reference angle of 23 degrees.  The side we are looking for is the hypotenuse of that triangle.  The trig ratio that relates the side opposite a reference angle to the hypotenuse of the right triangle is the sin ratio.  Setting it up using our values:

sin(23)=\frac{78.4}{x}, where x is the unknown length of the hypotenuse.  Solving for x:

x=\frac{78.4}{sin(23)}

Make sure your calculator is in degree mode before entering this in.  You will get a length of the hypotenuse as 200.649 feet, so choice A.

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3 years ago
WILL MARK AS BRAINLIEST FOR THESE QUESTIONS.
laiz [17]

1.

Let the sandwich be represented by = x

Let the drink be represented by = y

As given, Joe charges $10.00 for two sandwiches and one drink, so equation becomes 2x+y=10    ....(i)

He charges $6.50 for one sandwich and one drink, so equation becomes x+y=6.50  ....(ii)

Subtracting (ii) from (i) we get

x=3.50

And as x+y=6.50

y=6.50-3.50=3.00

Hence, cost of a sandwich is $3.50 and a drink is $3.00

2.

the question is incomplete. coordinates are missing

3.

Let x represent the number of performances

cost = 8000+300x

revenue = 700x

To break even, the cost must be equal to the revenue.

8000+300x=700x

400x=8000

so x=20

Hence, 20 performances are needed to break even.

4.

Let us take x for 20% material, y for 50% material

\frac{20x+50y}{200}=30

20x+50y=6000    ......... (1)

Accounting for volumes to use, x+y=200 or x=200-y ................ (2)

Putting the value of x in (1)

20(200-y)+50y=6000

4000-20y+50y=6000

4000+30y=6000

30y=2000

y=66.67

x=200-y = 200-66.67 =133.33

Hence, 133.33 ml of 20% acetic acid and 66.67% of 50% acetic acid is needed.





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What is the solution to the equation 3/5(x+4/3)=1.04
Fudgin [204]

Answer:

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Step-by-step explanation

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