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Serjik [45]
3 years ago
9

Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bag

s of popcorn and three drinks. Zachary spends a total of $27.50 for four bags of popcorn and two 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 bag of popcorn and the price of a drink, to the nearest cent.
Define your variables: p = cost of 1 popcorn, d = cost of 1 drink
Write an equation for each purchase:
2p + 3d = 18.25
4p + 2d = 27.50.
Mathematics
1 answer:
damaskus [11]3 years ago
4 0

Answer:

The cost of 1 popcorn is $5.75

The cost of 1 drink is $2.25

Step-by-step explanation:

Hi there!

First, let´s write the system of equations:

2p + 3d = 18.25

4p + 2d = 27.50

Now, let´s take the first equation (for example, it can be any equation) and solve it for "p":

2p + 3d = 18.25

Subtract 3d to both sides of the equation:

2p = 18.25 - 3d

divide both sides of the equation by 2:

p = (18.25 - 3d)/2

Now let´s replace p = (18.25 - 3d)/2 in the second equation and solve it for d:

4p + 2d = 27.50

4(18.25 - 3d)/2 + 2d = 27.50

2(18.25 - 3d) + 2d = 27.50

Apply distributive property:

36.5 - 6d + 2d = 27.50

subtract 36.5 to both sides of the equation:

-4d = 27.50 - 36.50

-4d = -9

divide both sides of the equation by -4:

d = -9/-4 = 2.25

The cost of 1 drink is $2.25

To calculate the price of popcorn, let´s use the equation we obtained above isolating "p":

p = (18.25 - 3d)/2

p = (18.25 - 3(2.25))/2

p = 5.75

The cost of 1 popcorn is $5.75

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Explain proportionality to me 7th grade math ​
kari74 [83]

If two quantities <em>a</em> and <em>b</em> are directly proportional to one another, then both <em>a</em> and <em>b</em> change in the <u>same direction</u>.

For example, if the amount/volume of coffee I have in a cup is directly proportional to the total volume of the cup, then the larger the cup gets, the more coffee I can fill it with. On the other hand, if the cup gets smaller, the amount of coffee it can hold also gets smaller.

Both <em>a</em> and <em>b</em> don't necessarily change at the same rate, though, which means one of these needs to get appropriately scaled by some factor <em>k</em>, so that

<em>a</em> = <em>kb</em>

Continuing the coffee example: Suppose I only fill my cup halfway. If the total volume of the cup is <em>a</em>, then the amount of coffee I pour in is <em>b</em> = 1/2 <em>a</em>. So the relationship of these two quantities is governed by the equation,

<em>a</em> = 2<em>b</em>

and in this case, <em>k</em> = 2.

If instead <em>a</em> and <em>b</em> are inversely proportional, this means as one quantity changes, the other changes in the <u>opposite direction</u>.

Suppose I have two cups that I use for coffee that can both hold the same amount <em>k</em> if they are filled completely, but one cup is taller than the other. In order for both cups to be able to hold the same volume of coffee, the taller cup must have a thinner profile.

The cups are cylindrical, so that their volumes are equal to the products of the area of their base <em>a</em> and their height <em>b</em>. If one cup is twice as tall as the other, then for the smaller cup we could have

<em>ab</em> = <em>k</em>

and for the taller one,

<em>a</em> (2<em>b</em>) = <em>k</em>

But in order to get the same volume, the quantity <em>a</em> for the shorter cup must be cut in half to preserve equality:

(1/2 <em>a</em>) (2<em>b</em>) = <em>ab</em> = <em>k</em>

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5 0
3 years ago
Help me fill in the blanks please help
agasfer [191]

The missing values in the inequality problem are;

A = -9

B = 72

C = 22

<h3>What is the explanation for the above?</h3>

5p - 8 (p + 1) > 16 .........................   (1) Given

5 (-10) - 8 (-10 +1) > 16 ...................... (2) Given

Where P is equal to 10 [Given in the second line as given in equation 2 above; Hence,

Substitute 10 for p

⇒ 5 (-10) - 8(-10+1)>  16

⇒ -50 -8(-9) > 16

⇒ -50 + 72 > 16

Hence

22 > 16 → T

Please note that T is symbolic of "True" that is

it is true that 22 is greater than 16.

Learn more about inequality problems:

brainly.com/question/11613554

#SPJ1

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