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
olganol [36]
3 years ago
6

Carlos ran a concession stand last Saturday and made $63.90 from selling a total of 41 hot dogs and hamburgers. Each hot dog sol

d for $1.40 and each hamburger sold for $2.70. Which system of equations can be used to determine the number of hot dogs, x, and hamburgers, y, that were sold?
Mathematics
1 answer:
Keith_Richards [23]3 years ago
6 0

The number of hot dogs, x is 36 and hamburgers, y is 5 were sold

Step-by-step explanation:

Carlos ran a concession stand last Saturday and made $63.90 from

a total of 41 hot dogs and hamburgers. Each hot dog sold for $1.40

and each hamburger sold for $2.70

1. The number of hot dogs is x, and hamburgers is y

2. He made $63.90 from a total of 41 hot dogs and hamburgers

3. Each hot dog sold for $1.40 and each hamburger sold for $2.70

We need to find the number of hot dogs and hamburgers, that were sold

∵ The number of hot dogs is x, and hamburgers is y

∵ He sold 41 hot dogs and hamburgers

∴ x + y = 41 ⇒ (1)

∵ Each hot dog sold for $1.40 and each hamburger sold for $2.70

∵ He sold x hot dogs and y hamburgers

∵ He made $63.90 from sold them

∴ 1.4 x + 2.7 y = 63.9 ⇒ (2)

Let Us solve the system of equations to find x and y

Multiply equation (1) by -2.7 to eliminate y

∵ (-2.7)x + (-2.7)y = (-2.7)(41)

∴ -2.7 x - 2.7 y = -110.7 ⇒ (3)

- Add equations (2) and (3)

∴ -1.3 x = -46.8

- Divide both sides by -1.3

∴ x = 36

Substitute the value of x in equation (1) to find y

∵ x + y = 41 ⇒ (1)

∴ 36 + y = 41

- Subtract 36 from both sides

∴ y = 5

The number of hot dogs, x is 36 and hamburgers, y is 5 were sold

Learn more:

You can learn more about system of equations in brainly.com/question/3739260

#LearnwithBrainly

You might be interested in
Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?
Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

sec^4 x + sec^2 x tan^2 x - 2 tan^4 x

Required

Simplify

(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2

Represent sec^2x with a

Represent tan^2x with b

The expression becomes

a^2 + ab- 2 b^2

Factorize

a^2 + 2ab -ab- 2 b^2

a(a + 2b) -b(a+ 2 b)

(a -b) (a+ 2 b)

Recall that

a = sec^2x

b = tan^2x

The expression (a -b) (a+ 2 b) becomes

(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)

..............................................................................................................................

In trigonometry

sec^2x =1  +tan^2x

Subtract tan^2x from both sides

sec^2x - tan^2x =1  +tan^2x - tan^2x

sec^2x - tan^2x =1

..............................................................................................................................

Substitute 1 for sec^2x - tan^2x in (sec^2x -tan^2x) (sec^2x+ 2 tan^2x)

(1) (sec^2x+ 2 tan^2x)

Open Bracket

sec^2x+ 2 tan^2x ------------------This is an equivalence

(secx)^2+ 2 (tanx)^2

Solving further;

................................................................................................................................

In trigonometry

secx = \frac{1}{cosx}

tanx = \frac{sinx}{cosx}

Substitute the expressions for secx and tanx

................................................................................................................................

(secx)^2+ 2 (tanx)^2 becomes

(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2

Open bracket

\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})

\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}

Add Fraction

\frac{1 + 2sin^2x}{cos^2x} ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

sin^2x + cos^2x= 1

Make sin^2x the subject of formula

sin^2x= 1  - cos^2x

................................................................................................................................

Substitute the expressions for 1  - cos^2x for sin^2x

\frac{1 + 2(1  - cos^2x)}{cos^2x}

Open bracket

\frac{1 + 2  - 2cos^2x}{cos^2x}

\frac{3  - 2cos^2x}{cos^2x} ---------------------- This is another equivalence

8 0
3 years ago
Please answer this question!!<br><br>thanks xx
Simora [160]
180-(180-49-48)
180-(83)
97

180-((180-141)+(180-76))
180-(39+104)
180-143
137

180-((180-101)+60)
180-(79+60)
180-139
41

360-147-79
213-79
139

180-(360-109*2)
180-(360-218)
180-142
38

(180-118)/2
62/2
31

Hope this helps :)
7 0
3 years ago
Need for a test rn help !!
Law Incorporation [45]

Answer:

26.6 mi^2

Step-by-step explanation:

3 0
3 years ago
The security guard for a sports store is making her rounds. She walks down 1 flight down to men’s clothing, then she walks up 2
Verdich [7]

Answer: There is no clothing

Step-by-step explanation:

It is a sports store

7 0
2 years ago
I need the steps and solution <br>-10x + 5y = 10 <br>x - 5y = -28​
natta225 [31]

−10x+5y=10

x−5y=−28

Rewrite equations:

x−5y=−28

−10x+5y=10

Step: Solve:

x−5y=−28

x−5y+5y=−28+5y(Add 5y to both sides)

x=5y−28

Step: Substitute:

−10x+5y=10

−10(5y−28)+5y=10

−45y+280=10(Simplify both sides of the equation)

−45y+280+−280=10+−280(Add -280 to both sides)

−45y=−270

−45y

−45

=

−270

−45

(Divide both sides by -45)

y=6

Step: Substitute:

x=5y−28

x=(5)(6)−28

x=2(Simplify both sides of the equation)

Answer:

x=2 and y=6

6 0
3 years ago
Other questions:
  • What are the properties of 8×51
    13·1 answer
  • The moon is about 240,000 miles from earth what is the order of magnitude of this number
    10·2 answers
  • What’s the slope of the line?
    10·2 answers
  • Driving from oban to stranraer a driver averages 8 miles per gallon of fuel. if fuel costs 83 cents a gallon how much will be th
    11·2 answers
  • A hockey goalie stops 37 out of 40
    11·2 answers
  • What pair of numbers has a gcf of 3
    10·1 answer
  • Sharla has 1/6
    14·2 answers
  • Consider the function f(x)=x^2-5. If g(x)=f(x-7), what can be said about g(x)? check all that apply
    11·1 answer
  • The table below contains data on how many pages were read for homework in Mr. Kaplinsky's third period. The equation of the line
    5·1 answer
  • Get really big brain for this
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!