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
In my pocket I have 8 quarters and 6 dimes. What fractional portion of the coins in my pocket are dimes
marin [14]

im pretty sure the answer is 3/4

7 0
3 years ago
Read 2 more answers
For his craft project, James bought 1010 10 10 pieces of ribbon that were each 2.1 feet2.1\text{ feet} 2.1 feet 2, point, 1, sta
BlackZzzverrR [31]

Answer:

<h2>Total yards of ribbon bought is 6.993yards of ribbon</h2>

Step-by-step explanation:

Total pieces of ribbon James bought for his craft project = 10pieces. If each pieces of ribbon were 2.1feet long, the total number of feet for 10ribbons is expressed as;

= 10 * 2.1\\= 21feets

Converting 21 feets to yards;

1 feet = 0.333yard

21feets = x

x = 21feet * 0.333\\= 6.993yards

Total yards of ribbon bought is 6.993yards of ribbon

3 0
3 years ago
John has less than 15 video games what is the inequality?
lidiya [134]

Answer: well, we don't have another number so i'll use variables

VG < 15

An easy way to remember what is the lesser value is to think of an alligator; the alligator wants to eat the bigger prey so in your case the bigger prey would be 15.

6 0
3 years ago
Find the area of the region that lies inside the first curve and outside the second curve. r = 6 − 6 sin θ, r = 6
yan [13]
Each curve completes one loop over the interval 0\le t\le2\pi. Find the intersections of the curves within this interval.

6-6\sin\theta=6\implies 1-\sin\theta=1\implies \sin\theta=0\implies \theta=0,\theta=\pi

The region of interest has an area given by the double integral

\displaystyle\int_\pi^{2\pi}\int_6^{6-6\sin\theta}r\,\mathrm dr\,\mathrm d\theta

equivalent to the single integral

\displaystyle\frac12\int_\pi^{2\pi}\bigg((6-6\sin\theta)^2-6^2\bigg)\,\mathrm d\theta

which evaluates to 9\pi+72.

8 0
3 years ago
Based on the tables, at what point do the lines y = 3x - 2 and y = -5x - 10 intersect?
Pepsi [2]
Intersect at where x=x and y=y
see where they have the same x and y values
that is at x=-1 and y=-5
intersect at (-1,-5)
8 0
3 years ago
Other questions:
  • Mrs. Smith’s wrote the number 43.38 on the board for a class discussion on place value. Explain the relationship between the two
    5·2 answers
  • 118 - [121 - (11 × 11) - (-4) - 3 - 9 - 2]​
    12·1 answer
  • Pam has monthly mortgage payment of $750. Her annual property taxes are $1200,her PMI is $55/month, and her homeowners insurance
    7·1 answer
  • You might need:
    7·1 answer
  • Geometry help please!
    10·1 answer
  • The stores markup on a wholesale item is 40%. The store is currently having a sale, and the item sales for 25% off the retail pr
    15·1 answer
  • 4. Solve. x² – 81 = 0 (1 point) 0 –9 –9, 9 9
    13·2 answers
  • Helllppppppp please
    11·1 answer
  • Please help fast!!!! Find the seventh term of the geometric sequence if a1=7 and r=3
    13·1 answer
  • How is HL related to KHF? Explain.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!