On a family outing, Tyler bought 5 cups of hot cocoa and 4 pretzels for
$18.40. Some of his family members would like a second serving, so he
went back to the same food stand and bought another 2 cups of hot cocoa
and 4 pretzels for $11.20.
Here is a system of equations that represent the quantities and constraints
in this situation.
5c + 4p = 18.40
2c + 4p - 11.20

If we add the second equation to the first equation, we have a new equation: 7c + 8p = 29.60
Explain why the same (c, p) pair that is a solution to this new equation.

Answers

Answer 1

9514 1404 393

Answer:

  the properties of equality tell you so

Step-by-step explanation:

A couple of properties of equality come into play here:

the addition property of equalitythe substitution property of equality

Each of the properties of equality tells you an operation you can perform on an equation without changing the values of the variables that satisfy that equation.

If we start with the equation ...

  5c + 4p = 18.40

and we add 11.20 to both sides, we have not changed the values of the variables that satisfy this equation. This is the addition property of equality.

  (5c +4p) +11.20 = (18.40) +11.20

The substitution property of equality says I can substitute anything for its equal. The second given equation tells me that 2c +4p = 11.20. This means I can use 2c+4p wherever 11.20 might be found without changing any variable values. In the equation we got from addition, we can now make this substitution, and we have ...

  (5c +4p) +(2c +4p) = (18.40) +(11.20)

  7c +8p = 29.60 . . . . . . . collect terms

We obtained this equation using properties of equality that guarantee solutions to these equations are not altered by the process.

_____

*Additional comment

Technically, by doing the "collect terms" step, we have made the assumption that the values of c and p that satisfy the first equation are the same as the values of c and p that satisfy the second equation. This is usually the case we're interested in.


Related Questions

Helpppppppopooppp pleassseee

Answers

Answer:

point p. ok. vrvxfff77t.

PLEASE I NEED HELP ASAP!!
Aluminum bronze consists of copper and aluminum, usually in the ratio of 10:1 by weight. If an object made of this alloy weighs 77 pounds, how many pounds of aluminum does it contain?

Answers

Answer:

The correct answer is (A). Copper and aluminum in the ratio of 10:1 means 10 parts copper to 1 part aluminum.

Step-by-step explanation:

7 pounds of aluminum in aluminum bronze by by weight.

What is Ratio?

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

What is percentage?

The percentage is defined as the ratio expressed as a fraction of 100.

The percentage is denoted by sign of %.

For example, if XYZ scored 46% marks in his test, it means that he scored 46 marks out of 100. It is written as 46/100 in the fraction form and 46:100 in terms of ratio.

Aluminum bronze consists of copper and aluminum in the ratio of 10:1 by weight

The ratio of copper and aluminum in aluminum bronze = 10:1

Let, aluminum in aluminum bronze by weight = x pound

And copper in aluminum bronze by weight = 10x pound

Since object made of this alloy weighs 77 pounds

So, x + 10x = 77

11x = 77

x = 7

Hence, 7 pounds of aluminum in aluminum bronze by by weight

Learn more about Ratio here:

brainly.com/question/1504221

#SPJ2

Find the final price of a $150.00 guitar after a 40%
discount and 6% tax.

Answers

Answer:

$ 100?

Step-by-step explanation:

That's my answer

I am stuck on how to do this, can someone please help?
1. Compute the total, and then fill in the rest of the ratio table given the different quantities that
have been set to 100. Make sure to always use the numbers in the first row to avoid round off error. Note the header row with titles is not counted as the “first” row. The first one is done for you.

Answers

Answer:

whats the problem about addition or subtraction or what then ill help u and post in comments

Step-by-step explanation:

[tex]x^{2} -5x-6[/tex]

Answers

Answer:

[tex] {x}^{2} - 5x - 6 \\ (x - 6)(x + 1)[/tex]

I hope I helped you^_^

find all the zeros of the quadratic function y=x²-9x+20

Answers

Answer:

Roots: x = 5; x = 4

Step-by-step explanation:

Given the quadratic equation, x² -9x + 20 = 0

where a = 1, b = -9, and c = 20

Determine the nature and number of solutions based on the discriminant, b² - 4ac:  

b² - 4ac = (-9)² - 4(1)(20) = 1

Since b² - 4ac > 0, then it means that the equation will have two real roots.

Use the Quadratic Formula:

[tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

[tex]x = \frac{-(-9) +/- \sqrt{(-9)^{2} - 4(1)(20)} }{2(1)}[/tex]

[tex]x = \frac{9 +/- \sqrt{1}}{2}[/tex]

[tex]x = \frac{9 + 1}{2}; x = \frac{9 - 1}{2}[/tex]

[tex]x = \frac{10}{2}; x = \frac{8}{2}[/tex]

x = 5; x = 4

Therefore, the roots of the quadratic equation are: x = 5; x = 4.

What is the common difference in the arithmetic sequence 30, 27, 24, 21, 18, ...?

Answers

Answer:

common difference is 3 you take each number from left to rifht and subtract so thr answer is 15

The common difference is -3.

PLEASE SOME ANSWER QUICKLY!!!!

Answers

Answer:

D

Step-by-step explanation:

The range is the y-values of a function. In this case, it would be 2, 4, 9, 16

x-2y+z=2
bx+ay=3
-2y+z=-4
Choose appropriate values for a and b

Answers

Answer:

Attached

Step-by-step explanation:

Just for your reference, this question will get unlimited number of solutions, attached is a few examples I calculated from Excel. Have fun to pick one or create one to be your favorite.


Simplify: the square root 400/576

Answers

Answer:

5 / 6

Step-by-step explanation:

√( 400 / 576 )

= √400 / √576

= 20 / 24

= 5 / 6

Answer:

5/6

Step-by-step explanation:

The GCF is 16 then divide it by both of denominator and numerator

> 400÷16/576÷16

> 25/36

then write there exponential form a²+b², a²-b², a²/b²

> 5²/6²

Simplify or (Reduce) there exponent

> 5/6

A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 7 : 40 p.m. At this time, he started pumping gas into the tank. At exactly 7 : 45 , the tank was full and he noticed that he has pumped 12.3 gallons. What is the average rate of flow of the gasoline into the gas tank

Answers

Answer: 2.46 gallons per minute.

Step-by-step explanation:

12.3 divided by 5 is 2.46.

increase percent of $25; 300%

Answers

The answer is 75

25x3=75

in math, the word dilate means to

Answers

Answer: it means to make larger or smaller.

Step-by-step explanation:

it means to make larger or smaller.

Answer:

A dilation is a transformation that changes the size of a figure. It can become larger or smaller, but the shape of the figure does not change. ... Knowing the scale factor allows you to predict what the image will look like after the dilation.

Step-by-step explanation:

Find the midpoint between (-9, 3) and (5, 7). PLEASE SOLVE THIS QUICK!! DUE IN AN HOUR

Answers

Answer:

(-2,5)

Step-by-step explanation:

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

We know that mid - point of a line segment divides it into two equal parts, that is it divides the segment in the ratio of 1 : 1, so let's find the coordinates of the mid point of line segment joining points (-9 , 3) and (5 , 7).

let the coordinates of the points be x and y, now

[tex]m = 1[/tex]

[tex]n = 1[/tex]

[tex]x_2 = 5[/tex]

[tex]x_1 = - 9[/tex]

[tex]y_2 = 7[/tex]

[tex]y_1 = 3[/tex]

Using section formula :

value of x :

[tex]x = \dfrac{mx_2 - nx_1}{m + n} [/tex]

[tex]x = \dfrac{(1 \times 5) - (1 \times - 9)}{1 + 1} [/tex]

[tex]x = \dfrac{5 - ( - 9)}{2} [/tex]

[tex]x = \dfrac{5 + 9}{2} [/tex]

[tex]x = \dfrac{14}{2} [/tex]

[tex]x = 7[/tex]

value of y :

[tex]y = \dfrac{my_2 -ny_1 }{m+ n} [/tex]

[tex]y = \dfrac{(1 \times 7) - (1 \times 3)}{1 + 1} [/tex]

[tex]y = \dfrac{7 - 3}{2}[/tex]

[tex]y = \dfrac{4}{2} [/tex]

[tex]y = 2[/tex]

So, coordinates of the point which is midpoint of the given line is :

[tex] \boxed{ \boxed{ (7, 2)}}[/tex]

The answer pleaseeee

Answers

Step-by-step explanation:

given,

x = 12

y = 4

therefore according to

F. y = 1/3x

4 = 1/3×12 1×4 = 4

4 = 4

G. y = 3x

4 = 3(12) = 36

4 36

H. y = 48/x

4 = 48/12

4 = 4

J. y = x - 8

4 = 12 - 8

4 = 4

therefore, F , H and J represents this relationship.

hope this answer helps you dear! take care

Hi, Which statement is True?

Answers

Answer:

The second one is true

Step-by-step explanation:

Write168 to the nearest hundred

Answers

Answer:

200

Step-by-step explanation:

6 is closer to 10 than 0

Hi, wanted to know if this looks correct to you guys, please leme know?

Answers

Answer:

yep all looks good to me

Step-by-step explanation:

15 ) Kayla has 14.5% of her salary placed into an Individual
Retirement Account. What fraction is this? *
1/2
22/100
2/3
29/200

Answers

Answer:

29/200

Step-by-step explanation:

Turn all fractions into percentages by dividing the numerator by the denominator then multiply the quotient by 100 to get it in percent.

1/2 = 50%

22/100 = 22%

2/3 = 66.7%

29/200 = 14.5%

Now that we turned all fractions into percents, we can see that 29/200 is that answer since its percentage is 14.5%.

a patio is rectangular. Its length is 8.27 meters and it's width is 4.2 meters. what is the approximate perimeter of the patio?

Answers

Answer: P≈24.94m

Step-by-step explanation:

P=2(l+w)=2·(8.27+4.2)≈24.94m

Super simple, just don't know if I am right or not.

Answers

The answer is 100% true
When it is graphed it points up over x axis
See pic

PLS HELP ME UNDERSTAND THIS

Answers

Answer:

-1

Step-by-step explanation:

can be soled by substitution remember BEDMAS

can also be written like this

((-2)-2*(-0.5))^3

-1 is the answer
Calcutense this to that and ejejsjekw sueñen con la que me has mandado el video del día del año que me paso en el día del año pasado

solve 12.01 x 5.21

please help me!

Answers

Answer:

62,5721

Step-by-step explanation:

12,01 × 5,21

= 62,5721

12.01×5.211201/100×521/100(1201)(521)/100²625721/1000062.5721

Plz help I need help

Answers

Answer:

1.025

Step-by-step explanation:

divided 6.15 by 6 to get 1.025

what is the value of the 4 in 53.42

Answers

Answer:

The value of four is tenths. If you are stuck in a question like this, just draw a place value grid.

Answer:

tens so 4*10 = 40

Step-by-step explanation:

53.42

the value of 4 is 4*10=40

Pls help do all and I’ll brainlist you

Answers

Answer:

1. 28.7

2. 14.11

3. 35.3

4. 32.8

Step-by-step explanation:

you just multiply then round the nearest tenths.

if 25 articles cost $43.75 how much does each cost?​

Answers

Answer:

$1.75

Step-by-step explanation:

I had this question and got it right!

How do I evaluate this

Answers

Answer:

18

Step-by-step explanation:

Plug in 3 for x

2(3)^2

2(3*3)

2*9

18

Answer:

The answer is 18

Step-by-step explanation:

2x², x = 3

Evaluate 3

2(3)²

2 × 9 = 18

Thus, The answer is 18

-TheUnknownScientist 72

Given b(x)= (-3,7), state what the coordinates of this point will be of the following transformations are effected: 2b(x)

Answers

The point translated up 7 and left 3. This will cause the point to go from (-3,7) to (-6,14)

b. 60:45 and 4:3 why is it equivalent.​

Answers

Step-by-step explanation:

60:45 in fraction form is [tex]\frac{60}{45}[/tex], and reducing it to its simplest form by dividing the fraction by [tex]\frac{15}{15}[/tex] gives you:

[tex]\frac{60}{45}[/tex] ÷  [tex]\frac{15}{15}[/tex] = [tex]\frac{4}{3}[/tex]

Likewise, 4:3 in fraction form is [tex]\frac{4}{3}[/tex].

Therefore, 60:45 and 4:3 are equivalent.

Answer:

because both can be divided by 15

Step-by-step explanation:

60/15=4

45/15=3

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