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Paladinen [302]
3 years ago
12

John sales model boats from a booth at a local fair. He purchases each model boat from a distributor for five dollars and the lo

cal fair chargers him a baby and $80 John cells each model boat for $50. Write a system of equations to represent the situation
Mathematics
1 answer:
poizon [28]3 years ago
7 0

Answer and explanation:

Profit from sale of model boats = Sales -costs(costs of goods purchases + expenses or charges by the local fair)

John's profit from the sale of model boats can be represented by the equation:

P= 50x-(5x+80)

Where P is profit from the sale of the model boats and x is number of model boats bought and sold. The 80 is constant as it is a fixed cost paid to the local fair.

For example if John buys and sells 20 model boats, he would make profit of:

Substitute x=20 in equation above

P= 50×20-(5×20+80)

P=1000-180

P=$820

It could be said that John is in a very profitable business and his profit is also dependent on volume of sales because the lower his sales the closer he gets to making a loss and not profit

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Grant earns $5 for each magazine he sells.Write an equation in two variables showing the relationship between the number pf maga
slega [8]

Answer:

A=5m

Grant will make $60 from selling 12 magazines.

Step-by-step explanation:

Let m represent number of magazine sold and A represent amount of money earned.

We have been given that Grant earns $5 for each magazine he sells. So amount earned from m magazines would be 5 times m that is 5m dollars.

Now, we will equate total amount earned by Grant with A as:

A=5m

Therefore, our required equation would be A=5m.

To find the amount earned by Grant by selling 12 magazines, we will substitute m=12 in our equation as:

A=5(12)

A=60

Therefore, Grant will make $60 from selling 12 magazines.

3 0
3 years ago
(100) points!!!! Help please
inysia [295]

Answer:

\displaystyle a_8=142,11\ mg

Step-by-step explanation:

Geometric sequence

Each term in a geometric sequence can be computed as the previous term by a constant number called the common ratio. The formula to get the term n is

\displaystyle a_n=a_1r^{n-1}

where a_1 is the first term of the sequence

The problem describes Georgie took 275 mg of the medicine for her cold in the first hour and that in each subsequent hour, the amount of medicine in her body is 91% (0.91) of the amount from the previous hour. It can be written as

amount in hour n = amount in hour n-1 * 0.91

a)

This information provides the necessary data to write the general term as

\displaystyle a_n=275\ .\ 0.91^{n-1}

b)

In the 8th hour (n=8), the remaining medicine present is Georgie's body is

\displaystyle a_n=275\ .\ 0.91^{8-1}

\displaystyle a_n=275\ .\ 0.91^{7}

\boxed{\displaystyle a_8=142,11\ mg}

6 0
3 years ago
A sweet factory produces 5 different chocolate bars. the different flavors are always produced in the same proportions, for ever
IRISSAK [1]

a. There are 933 chocolate bars

b. There are 1200 chocolate bars

c. There are 1580 chocolate bars

<h3>How to calculate the number of chocolate bars</h3>

Since there are 5 different flavors,

let

  • x = orange flavored bars,
  • y = coconut flavored bars,
  • z = coffee flavored bars,
  • a = strawberry flavored bars and
  • b = honeycomb flavored bars and
  • X = total number of bars

Since the different flavors are always produced in the same proportions, for every 4 coconut flavored bars 5 honeycomb 6 orange 1 coffee and 4 strawberry

So, the ratio of their proportions are x:y:z:a:b = 6:4:2:1:5

So, the total ratio is T = 6 + 4 + 1 + 4 + 5 = 20

<h3>a. What is the total number of chocolate bars if there are 280 orange flavored bars?</h3>

Since we have 6 orange flavored bars, the ratio of orange flavored bars to total is 6/20

So, the amount of orange flavored bars is x = 6/20 × X

Making X subject of the formula, we have

X = 20x/6

So, if there are 280 orange bars, there will be

X = 20x/6

X = 20 × 280/6

X = 5600/6

X = 933.33

X ≅ 933 chocolate bars

So, there are 933 chocolate bars

<h3>b. What is the total number of chocolate bars if there are 960 coconut flavored bars?</h3>

Since we have 4 coconut flavored bars, the ratio of coconut flavored bars to total is 4/20

So, the amount of coconut flavored bars is y = 4/20 × X

Making X subject of the formula, we have

X = 20y/4

So, if there are 960 coconut flavored bars, there will be

X = 20y/6

X = 20 × 960/4

X = 5 × 240

X = 1200 chocolate bars

So, there are 1200 chocolate bars

<h3>c. What is the total number of chocolate bars if there are 79 coffee flavored bars?</h3>

Since we have 1 coffee flavored bars, the ratio of coffee flavored bars to total is 1/20

So, the amount of coconut flavored bars is z = 1/20 × X

Making X subject of the formula, we have

X = 20z

So, if there are 79 coffee flavored bars, there will be

X = 20z

X = 20 × 79

X = 1580 chocolate bars

So, there are 1580 chocolate bars

Learn more about ratio here:

brainly.com/question/1127546

#SPJ1

7 0
1 year ago
Lena bought 14 yards of wire. How many inches of wire did she buy? ( 1 yard =36 inches)
KengaRu [80]

Answer:

504 inches

Step-by-step explanation:

Multiply 14 by 36 and get your answer

3 0
2 years ago
Simplify the trigonometric expression. 1/1+ sin theta + 1/1-sin theta A, 2 cos^2 theta B. 2 sec^2 theta C. 2 csc^2 theta D. 2 co
Ganezh [65]
So the problem ask to simplify the trigonometric function in your problem and base on the expression and using the theory in simplifying trigonometric function, the answer would be letter B. 2 sec^2 theta. I hope you are satisfied with my answer and feel free to ask for more  
3 0
2 years ago
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