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
larisa86 [58]
3 years ago
9

Mason and Christian go to the movie theater and purchase refreshments for their friends. Mason spends a total of $45.75 on 3 bag

s of popcorn and 6 drinks. Christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.
Mathematics
1 answer:
Blababa [14]3 years ago
4 0

Answer:

  • A bag of popcorn costs $10.25
  • One drink costs $2,5

Step-by-step explanation:

Let the cost of a bag of popcorn=p

Let the cost of a drink=d

Mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks.

  • Therefore: 3p+6d=45.75

Christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks.

  • Therefore: 6p+4d=71.50

The required system of equations is:

  • 3p+6d=45.75
  • 6p+4d=71.50

Multiply the first equation by 2 to eliminate p

6p+12d=91.5

6p+4d=71.50

Subtract

8d=20

d=20/8=$2.5

Substitute d=2.5 into any of the equations to obtain p.

6p+12d=91.5

6p+12(2.5)=91.5

6p=91.5-12(2.5)

6p=91.5-30

6p=61.5

Divide both sides by 6

p=$10.25

Therefore:

  • A bag of popcorn costs $10.25
  • One drink costs $2,5

You might be interested in
An electronic product contains 48 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the
BigorU [14]

Answer:

0.6173 = 61.73% probability that the product operates.

Step-by-step explanation:

For each integrated circuit, there are only two possible outcomes. Either they are defective, or they are not. The integrated circuits are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

An electronic product contains 48 integrated circuits.

This means that n = 48

The probability that any integrated circuit is defective is 0.01.

This means that p = 0.01

The product operates only if there are no defective integrated circuits. What is the probability that the product operates?

This is P(X = 0). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{48,0}.(0.01)^{0}.(0.99)^{48} = 0.6173

0.6173 = 61.73% probability that the product operates.

5 0
3 years ago
Select the correct answer from each drop-down menu.
ExtremeBDS [4]

Answer:

7

Step-by-step explanation:

8 0
2 years ago
help me (a) The total cost of rent is determined by recording x months of rent at $1400 per month, plus a $150 application fee.
xxTIMURxx [149]

Answer:

$1400x  + $150

Step-by-step explanation:

Let the total cost of rent used for a month be $1400 plus a $150 application fee.

This means that;

Total cost (1 month) = $1400(1) + $150 = $1550

TO calculate the cost for x months, we will simply multiply x with the cost of rent for 1 month as shown.

The cost of rent for x month = 1400x * $150

The cost of rent for x month = $1400x  + $150 (application fee are paid only once)

6 0
2 years ago
Can someone help with this please?
Norma-Jean [14]

Answer:

n=11

Step-by-step explanation:

By inspection,we see that an output is obtained by subtracting 3 from an input and the next consecutive output will follow a pattern of a difference of odd numbers that is 9+5=14

so n=14 and 14-3=11

8 0
2 years ago
What is 10 times as much as 60?
vfiekz [6]
10 time as much of something is basically just multiplication, so all you have do is multiply 60x10 which equals 600 :)
7 0
3 years ago
Read 2 more answers
Other questions:
  • tony began putting together a rectangular puzzle.he completed the top edge and left edge of the puzzle, each piece is a square t
    13·1 answer
  • I was at the store and saw two sizes of avocados being sold. The regular size sold for $0.79 each. For what prices would the lar
    5·1 answer
  • After filling a gas tank the odometer read 39.007.2 after the next filling it read 39.469.2 it took 17.5 gal to fill the tank, h
    5·1 answer
  • Which one of the following statements is NOT true of a free-falling object? An object in a state of free fall ____.
    6·1 answer
  • Prime factores of 36​
    8·1 answer
  • Need help! Urgent. Giving lots of points for this
    11·1 answer
  • Got this one wrong need help
    8·1 answer
  • Solve for b, i already solved for A <br> will give brainliest
    7·1 answer
  • The temperature falls from 10°F to -15° F. What is the difference in these<br> temperatures?
    15·1 answer
  • Fruit Vendor A sells oranges for $7.00 a dozen. Fruit Vendor B sells the oranges at 5 for $3.00. Determine which fruit vendor gi
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!