1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Find the gradient, picture below
hoa [83]

Answer:

\frac{dy}{dx}  =  \frac{13}{8}

Step-by-step explanation:

y = 2x + 6 {x}^{ -  \frac{1}{2} }  \\  \frac{dy}{dx} = 2 + 6( -  \frac{1}{2}) {x}^{ -  \frac{1}{2} - 1 }   \\  \frac{dy}{dx}  = 2 - 3 {x}^{ -  \frac{3}{2} }  \\ \frac{dy}{dx}  = 2 -  \frac{3}{ \sqrt{ {x}^{3} } }

When x = 4,

\frac{dy}{dx}  = 2 -  \frac{3}{ \sqrt{ {4}^{3} } }  \\  =  \frac{13}{8}

3 0
2 years ago
Read 2 more answers
Kaylee invested $910 in an account paying an interest rate of 2.6% compounded
Nikitich [7]

Answer:

$1,179

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

A=P(1+\frac{r}{n} )^{nt}

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em>t = time</em>

<em />

First, lets change 2.6% into a decimal:

2.6% -> \frac{2.6}{100} -> 0.026

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

A=910(1+\frac{0.026}{4})^{4(10)}

A=1,179.21

The account balance after 10 years will be $1,179

8 0
3 years ago
May someone please help me with this :)
adoni [48]

Answer:

24

Step-by-step explanation:

6+8=14 14+10=24

4 0
3 years ago
Find the area of the figure shown below.<br> 10 cm<br> 5 cm<br> 17 cm
stira [4]

Answer:

where is the figure?

Step-by-step explanation:

I can't see a figure

8 0
3 years ago
Read 2 more answers
A hockey coach was taking her team out to a picnic lunch to celebrate their first win. She made 15 sandwiches, 6 of which were t
alexira [117]

The probability that exactly 3 of the chosen sandwiches are turkey is; 0.004

<h3 /><h3>How to find the probability combination?</h3>

We are given;

Total number of sandwiches = 15

Number of sandwiches that were turkey = 6

Now, she selects 6 of the sandwiches and we want to find the probability that exactly 3 are turkey.

Now, number of ways of selecting 6 sandwiches is; 15C6

Number of ways of selecting 3 turkey's out of the 6 chosen is; 6C3

Thus, the probability that exactly 3 of the chosen sandwiches are turkey is; 6C3/15C6 = 20/5005 = 0.004

Read more about Probability combination at; brainly.com/question/3901018

#SPJ1

7 0
1 year ago
Other questions:
  • In each of the following statements, identify the boldfaced and underlined number as the value of a population parameter or a sa
    5·1 answer
  • Select the postulate or theorem that you can use to conclude that the triangles are similar.
    7·1 answer
  • (6x2y + 4xy2 − 2y3 + 6) + (x2y + 3y3 − 5)
    10·1 answer
  • Lines m and n are perpendicular. If the slope of m is zero, then the slope of n is
    13·2 answers
  • Use the equation below to find v, if u=16, a=11, and t=2<br><br> V=u+at
    6·1 answer
  • Write each ratio as a fraction ?
    7·1 answer
  • A pump can fill a 750 gallon tank in 35 minutes.how long will it take to fill 1200 gallons
    15·1 answer
  • A hypothesis test was conducted to test whether has been an increase in the proportion of students that attend college right aft
    15·1 answer
  • Kimberly bought a hat that costs 10 dollars and a watch that costs 19 dollars. At the counter, she received a discount. If she o
    6·1 answer
  • A bank manager wants to encourage new customers to open accounts with principals of at least $3,000. He decides to make a poster
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!