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
Gennadij [26K]
3 years ago
14

After the booster club sold 40 hotdogs at a football game, it had 90$ in profit. After the next game, it had sold a total of 80

hotdogs and a total of $210 in profit. Which equation models the total profit, y, based on the number of hotdogs sold, x?
Mathematics
1 answer:
sergiy2304 [10]3 years ago
3 0
Let's first establish what we already know for this problem.

x = total number of hotdogs sold
y = total profit from total sales of hotdogs

Let's also establish the other equations which we will require in order to solve this problem.

Equation No. 1 -
Profit for 40 hotdogs = $90 profit

Equation No. 2 -
Profit for 80 hotdogs = $210 profit

STEP-BY-STEP SOLUTION

From this, we can use the formula y = mx + b & substitute the values for x & y from one of the two previous equations into the formula in order to obtain the values of m & b for the final equation. Here is an example of the working out as displayed below:

Firstly, using the first or second equation, we make either m or b the subject. Here I have used the first equation and made m the subject:

Equation No. 1 -
y = mx + b
90 = m ( 40 ) + b
40m = 90 - b
m = ( 90 - b ) / 40

Now, make b the subject in the second equation as displayed below:

Equation No. 2 -
y = mx + b
210 = m ( 80 ) + b
210 = 80m + b
b = 210 - 80m

Then, substitute m from the first equation into the second equation.

Equation No. 2 -
b = 210 - 80m
b = 210 - 80 [ ( 90 - b ) / 40 ]
b = 210 - [ 80 ( 90 - b ) / 40 ]
b = 210 - 2 ( 90 - b )
b = 210 - 180 - 2b
b - 2b = 30
- b = 30
b = - 30

Now, substitute b from the second equation into the first equation.

Equation No. 1 -
m = ( 90 - b ) / 40
m = ( 90 - ( - 30 ) / 40
m = ( 90 + 30 ) / 40
m = 120 / 40
m = 3

Through this, we have established that:

m = 3
b = - 30

Therefore, the final equation to model the final profit, y, based on the number of hotdogs sold, x, is as follows:

y = mx + b
y = ( 3 )x + ( - 30 )

ANSWER:
y = 3x - 30
You might be interested in
Solve the following equations 19=7+y
Svetlanka [38]
Subtract the 7 from both sides,
you are left with
11=y
5 0
3 years ago
Read 2 more answers
At a self-service gas station, 40% of customers pump regular gas, 35% pump midgrade, and 25% pump premium gas. Of those who pump
Aleks04 [339]

Answer:

0.150,0.595

Step-by-step explanation:

Given that at a self-service gas station, 40% of customers pump regular gas, 35% pump midgrade, and 25% pump premium gas. Of those who pump regular, 30% pay at least $30. Of those who pump midgrade, 50% pay at least $30. And of those who pump premium, 60% pay at least $30.

               Regular gas          Midgrade         Premium gas      Total

Percent      40                            35                     25                   100

atleast 30   30%                         50%                 60%

a) The   probability that the next customer pumps premium gas and pays at least $30

=0.25*0.60\\=0.150

b)        the probability that the next customer pays at least $30

= P(regular and pays atleast 30%)+P(premium and pays atleast 30%)+P(midgrade and       pays atleast 30%)

=0.40*0.30+0.35*0.50+0.25*0.60\\=0.12+0.175+0.30\\=0.595                  

6 0
3 years ago
The ratio 3:8 12:32 omg do not like this comon core math
tensa zangetsu [6.8K]
Both ratios are equal
7 0
2 years ago
Read 2 more answers
A circle has a radius of 4 ft. What is the area of the sector formed by a central angle measuring 3π2 radians? Use 3.14 for pi.
Vikki [24]

Answer:

The answer is 37.68 I just took the test.

5 0
3 years ago
Read 2 more answers
The digit 1 in which number represents a value of 10,000
nika2105 [10]
The digit one is in the "ten thousands" column
3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the sign of the product (−2)(4)(−6)(−3)?
    5·2 answers
  • 5x - 4 = -3x + 12. Solve for x
    7·1 answer
  • Help me please. I really need help
    9·1 answer
  • 20 grams is 60% of what weight
    6·1 answer
  • Find the median of the data Weight (in ounces) of puppies in litter 17, 15, 19,18,17,16,22 Median: [?] oz​
    11·1 answer
  • Which two statements describe processes most likely to be involved in the
    5·1 answer
  • It is not B so plz help me
    6·2 answers
  • A baby gains about 15 pounds each month. About how much weight will the baby have gained after 6 months? a. About 7.5 pounds b.
    9·2 answers
  • A line passes through the point (-6,-9) and has a slope of . Write an equation in slope-intercept form for this line.
    12·1 answer
  • Which of the following notes is G?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!