arper went into a movie theater and bought 10 bags of popcorn and 6 drinks, costing a total of $79. Damian went into the same movie theater and bought 3 bags of popcorn and 5 drinks, costing a total of $36.50. Write a system of equations that could be used to determine the price of each bag of popcorn and the price of each drink. Define the variables that you use to write the system.

Answers

Answer 1
Answer:
The price of a drink = $4
The price of a bag of popcorn = $5.5

Step-by-step explanation:

Let p represent popcorn and d represent drink
Harper bought 10 bags of popcorn and 6 drinks and paid $79 ➡ 10p + 6d = $79
Damian bought 3 bags of popcorn and 5 drinks and paid $36.50 ➡ 3p + 5d = $36.50
Now multiply first equation by -3 and second equation by 10
-3 × (10p + 6d) = $79 ➡ -30p - 18d = -$237
10 × (3p + 5d) = $36.50 ➡ 30p + 50d = $365
Now add the new equationd
30p + 50d -30p - 18d = $365 - $237 (-30p will eliminate 30p)
32d = $128 divide both sides of the equation by 32
32 ÷ 32d = 32 ÷ $128 ➡ d = 4
If d = 4 that means a drink costs $4 we can use this information to find the price of a bag of popcorn
3p + 5d = $36.50 (replace d with 4)
3p + 4×5 = $36.50
3p + 20 = $36.50
3p = $36.50 - 20
3p = 16.50 divide both sides by 3
p = $5.5
Answer 2

Answer:

popcorn is 5.5 and drink is 4

Step-by-step explanation:

It just is my g


Related Questions

= Simplify the following algebraic expressions given below into their equivalent standard forms.

(x + 10)(x + 10)

Answers

Answer:

https://tex.z-dn.net/?f=(x%2B10)%5E%7B2%7D%20

Step-by-step explanation:

Three paintings are shaped like an 8-foot square a 7-foot by 4-foot rectangle and a triangle with 6-foot base and height of 7 feet. If those paintings are hung together on the outside of the building how much of the building s wall they cover together ?

Answers

Answer:

113 square feet

Step-by-step explanation:

the total area covered can be determined by adding the area of the rectangle, triangle and square together

Area of a square = length² = 8² = 64 ft²

Area of a rectangle = length x width = 7 x 4 = 28 ft²

Area of a triangle = 1/2 x base x height = 1/2 x 6 x 7 = 21 ft²

64 + 28 + 21 = 113 ft²


The value, V(t), of a baseball card increases according to the function V(t) = P(1.045)', where P is the purchase price of the
baseball card and t is the time, in years since the card was purchased. By what percent does the value of the card increase each
year'?
1 4.5%
2 45%
3 95.5%
4 145%

Answers

The Percentage increase in the purchase price each year is 4.5%.

The given function is:

[tex]V(t)=P(1.045)^t[/tex]

Where P is the purchase price of the baseball card and t is the time.

What is a function?

A function is a rule that establishes a relation between two variables.

[tex]V(1)=P(1.045)^1\\V(1)=1.045P[/tex]

[tex]V(2)=P(1.045)^2\\V(2)=1.092025P[/tex]

Percentage increase in the purchase price each year

=[tex]\frac{V(2)-V(1)}{V(1)} *100[/tex]

[tex]=\frac{1.092025P-1.045P}{1.045P} *100[/tex]

[tex]=4.5%[/tex]%

Hence, the Percentage increase in the purchase price each year is 4.5%.

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A triangle has two 12centimeter sides
. What are the possible lengths of third side?

Answers

Answer:

Step-by-step explanation:

if the two sides are 12, the third will have to be shorter so it could be:

( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 )

good luck!

can you choose me brainliest? :D

An airplane altitude in feet during its descend can be found using the function f(x)=-200x+20,000. After new government regulations become law the descent is now modeled by the function g(x)=-200x+20,500. Which statement describes the change?

Answers

Answer:

The airplane starts its descent from an altitude 500 feet higher.

Step-by-step explanation:

Given that:

F(x) = - 200x+20,000

g(x) = -200x+20,500

The functions are written in slope intercept format :

With a negative slope, the intercept gives the point which the rate of change begins in the vertical axis :

The slope is -200 ; which means that the descent rate of the airplane is 200

The intercept value however changes from 20,000 in f(x) to 20500 in g(x). This means that the height at which descent starts is now at a height of 20500 which is (20500 - 20000) = 500 miles higher than before.

surface area of a rectangular prism with length 11 meters, width 5 meters, and height 14 meters

Answers

Answer:

Step-by-step explanation:11

When rolling a number cube, what is the probability of rolling a 2 or an even number. Express your answer as a fraction in lowest terms

Answers

Answer:

https://www.sketchywebsite.net/

Step-by-step explanation:

What is true about the slopes of lines that are perpendicular?
A They have opposite signs
B They are reciprocals of each other
C They have opposites signs and are reciprocals of each other
D They are exactly the same

Answers

C, They have opposites signs and are reciprocals of each other.

HELPP
giving brainliest

Answers

Answer:

4 feet 10 in

Step-by-step explanation:

58/12= 4 10/12= 4 feet 10 in

Answer:

4ft 10in

Step-by-step explanation:

58/12 = 4 10/12

Pls help with thissss

Answers

10.3 if you divide 43 and 11 you round and get 10.3

which angle is supplementary to.... asap plz

Answers

Angle CGA supplementary angles add up to 180°

Answer:

Angle AGC

Step-by-step explanation:

Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees. ... For example, a 50-degree angle and a 40-degree angle are complementary; a 60-degree angle and a 120-degree angle are supplementary

20% of ______ is 120​

Answers

Answer:600

Step-by-step explanation:

Answer:

20

___ x X = 120

100

x100       x 100

20x = 120

divide by 20 on both sides.

x = 6

Find the profit or loss if:
Cost price = $19.85 Selling price = $20.20
tell me also wether it’s a profit or loss

Answers

Answer:

It would be a profit  of .35 cents

Step-by-step explanation:

Answer:

it is a profit by 0.35 cents

Step-by-step explanation:

That is becuase it costed you 19.85 so you ost 19.85 and gain 35 cents becuase you are selling it for a higher price

if 2f(x)-3f(1/x)=x^2 determine f(2)

Answers

-7/4
hope this helped

What is the PE of an object that is 15kg that is 5.0 M above the ground?

Answers

Answer:

735 J

Step-by-step explanation:

The potential energy of a body can be found by using the formula

PE = mgh

where

m is the mass

h is the height

g is the acceleration due to gravity which is 9.8 m/s²

From the question we have

PE = 15 × 9.8 × 5

We have the final answer as

735 J

Hope this helps you

In the diagram below, BC = QR = x, AC = PR = y, and triangle PQR is a right
triangle. Use the drop-down menus to complete the proof that if the equation
22 + y2 = z2 is true of the side lengths in triangle ABC, then triangle ABC must be a right
triangle.
P
y у
y
B
R
х
Q
x2 + y2 = 22
Triangle PQR is a right triangle
Click the arrows to cho
from each menu.
Triangle PQR is given to be a right triangle, so the Pythagorean theorem can be used to

Answers

Applying the Pythagorean theorem, we have ΔPQR ≅ ΔABC. then we would have: ∠ACB = ∠PRQ = 90°

What is the Pythagroean Theorem?

The pythagorean theorem states that the square of the longest side (hypotenuse) of a right triangle is always equal to the sum of the squares of the other two sides (legs) of the right triangle.

Since we know that ΔPQR is a right triangle, then:

x² + y² = PQ²

We are also given that x² + y² = z², so by substitution, we have:

z² = PQ², which makes both triangles have corresponding congruent sides. Therefore, ΔPQR ≅ ΔABC.

Using the corresponding parts of the congruent triangles, we can conclude that: ∠ACB = ∠PRQ = 90°.

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Helpppp asapppp I’ll give you a lot of points

Answers

Answer:

[tex]x = \frac{5a-2} {7+5a}\\[/tex]

Step-by-step explanation:

Given the expressions

[tex]x = \frac{5}{9y+5}....1\\y = \frac{5}{5a-2} ...2[/tex]

Substitute 2 into 1

[tex]x = \frac{5}{9(\frac{5}{5a-2} )+5} \\x = \frac{5}{(\frac{45}{5a-2} )+5} \\x = \frac{5}{\frac{45+5(5a-2)}{5a-2} } \\x= \frac{5}{\frac{35+25a}{5a-2} }\\x = \frac{5(5a-2)} {35+25a}\\x = \frac{5(5a-2)} {5(7+5a})\\\\x = \frac{5a-2} {7+5a}\\[/tex]

HELP PLEASE ANSWER I NEED HELP

Answers

Answer:

x=30

Step-by-step explanation:

x/5-16=-10

x/5=-10+16

x/5=6

x=6×5

x=30

The price of 7​-minute phone call is ​$.105 What is the price of 18 ​-minute phone​ call?
The price of 18​-minute phone call is ​$

Answers

Answer:

$.27

Step-by-step explanation:

.105/7*18

Question below...15 points.

Answers

Answer: i think its c

Step-by-step explanation:

but im not totally sure

Answer:

B. s = 9 inches

Step-by-step explanation:

We are given a square with a perimeter of 36 inches, along with a key that the perimeter is given through the equation P = 4s, where "s" stands for the length of one side. We are then asked to find which number s is.

Perimeter is when you add 4 sides altogether, in our case we have 36 inches as our perimeter. Since 4s is the main factor as to how we got 36 inches, we need to set up one system equation.

P = 4s

36 = 4s

Now we need to find a number that multiplies with 4 to get us 36, simple as that. Let's get s alone to retrieve our answer :

36 = 4s

Divide 4 from both sides :

9 = s

s = 9

from edgunuity please help asap! image attached above​

Answers

It’s 4 I hope this helps


Explanation I took this in 9th grade so I know how to do this kind of stuff

name the property illustrated. 6 + (4+9) = (6 + 4) + 9

Answers

Answer:

associative property

Step-by-step explanation:

happy to help :)

Answer:

Associative Property

Step-by-step explanation:

The property says you can regroup the three numbers being added.

(a + b) + c = a + (b + c)

Either add a and b first, then add c, ...

or, add b and c first, then add that result to a.

Find 3[g(4)] if g(x) = -2x + 10

Answers

Answer:

6

Step-by-step explanation:

= 3[-2(4) + 10]

= 3(-8 + 10)

= 3(2)

The function is given as  g(x) = -2x + 10 then the solution of the 3[g(4)] would be equal to 6.

What is a function?

A function is a type of relation, or rule, that maps one input to a specific single output.

Functions that are formed by composing two or more functions in a way that one's output is another's input are called composite functions.

They are also called functions of functions.

We have to find 3[g(4)] if g(x) = -2x + 10

3[g(4)] = 3[-2(4) + 10]

3[g(4)]  = 3(-8 + 10)

3[g(4)]  = 3(2)

3[g(4)]  = 6

Learn more about function here:

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how do you solve 27.5% of 88

Answers

answer:

im getting different answers so  wait ill do it myself

Step-by-step explanation:

For an upcoming election, 500 registered voters were surveyed on a tax increase. 43% were for a tax increase and 51% were against a tax increase. The margin of error was 6%. What is an accurate conclusion from the poll?
a. Against a tax increase will win because it is above 50%.
b. The nal result is undecided because of the margin of error.
c. The nal result is undecided because percentages do not add up to 100%.
d. Against a tax increase will win because the margin of error will increase their percentage.

Answers

Against a tax increase because either way the margin of error may fall, against will still have more votes

D + -4 = 12
how do i find d?​

Answers

Answer: D=16

Add 4 to both sides

D=16

Answer:

Answer: 16

Step-by-step explanation:

Do 12 -(-4 to get D

12 -(-4 = 16

Answer the question in the picture?

Answers

Answer:

19

Step-by-step explanation:

we know the sides of a rhombus is all equal, so:

4(2x+4)=168

8x+16=168

8x=152

x=19

Please help ASAP ASAP

Answers

Answer:X=110

Step-by-step explanation:

When you divide 196 by 20 you get 9.8 so when you divide 1078 by 9.8 you get 110

I think that the answer is 110=x

Someone please tell me the answers to this please I beg you

Answers

1) 216
2) 203
3) 315
4) 256
5) 576
6) 440

Flora drew the following graph to answer the question. What was her mistake when she drew her graph?

Answers

Answer:

She drew the graph too steep, if she is going down at a constant rate of 300 ft per hour, at 1 hour she would be at 2,700 ft. it would take her about 10 hours to get down the mountain.

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