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
posledela
3 years ago
11

An electronics store makes a profit of $72 for every television sold and $90 for every computer sold. The manager’s target is to

make at least $360 a day on sales from televisions and computers. Write a linear inequality and graph the solutions. What are three possible solutions to the problem?

Mathematics
2 answers:
Musya8 [376]3 years ago
6 0
Answer: <span>A. (5, 2), (3, 3), and (1, 4) are three possible solutions. </span>

Explanation:

This is the set of answer choices for this problem:

<span>A. (5, 2), (3, 3), and (1, 4) are three possible solutions.
B. (4, 0), (2, 2), and (1, 1) are three possible solutions.
C. (3, 1), (2, 2), and (1, 0) are three possible solutions. .
D. (4, 0), (3, 3), and (1, 4) are three possible solutions. </span>

This is how you solve it.

1) name the variables:

t: number of tv sold
c: number of computer sold

2) model the profit = 72t + 90c

3) set the inequality:

The manager's target is to make at least $360 => profit ≥ 360

=> 72t + 90c ≥ 360

simplify dividing by 9 => 8t + 10c ≥ 40

simplify dividing by 2 => 4t + 5c ≥ 20

4) graph 4t + 5x ≥ 20

- draw the line 4t + 5c = 20

   notice that 5c = - 4t + 20 => c = (-4/5)t + 4

=> slope -4/5, c intercept 4

So, the solution is the region above the line 4t + 5c = 20, in the first quatrant ( t≥0, and c≥0)

5) use the set of answer choices to probe which are solutions:

<span>A. (5, 2), (3, 3), and (1, 4) are three possible solutions.

Use the inequality to probe each pair:

- point (5,2): 4(5) + 5(2) = 20 + 10 = 30 ≥ 36 => ok

-  point (3,3): 4(3) + 5(3) = 12 + 15 = 27 ≥ 36 => ok

- point (1,4): 4(1) + 5(4) = 4 + 20 = 24 ≥ 20 => ok

Therefore that is the answer.

Check how the other choices are discarded.

B. (4, 0), (2, 2), and (1, 1) are three possible solutions.

- point (1,1) is not solution: 4(1) + 5(1) = 4 + 5 = 9 which is not ≥ 20 => not solution.

C. (3, 1), (2, 2), and (1, 0) are three possible solutions. .


- point (1,0) is not solution: 4(1) + 5(0) = 4 + 0 = 4 which is not ≥ 20 => not solution.

D. (4, 0), (3, 3), and (1, 4) are three possible solutions.

- point (4,0) is not solution: 4(4) + 5(0) = 16 + 0 = 16 which is not  ≥ 20.
</span>

exis [7]3 years ago
4 0

the complete question in the attached figure

 

we have 

$72 ------------------------------------ > for every television sold

$90 ------------------------------------ > for every computer sold.

let 

x--------------------- > numbers of television sold

y--------------------- > numbers of computer sold 

then 

72x+90y >= $360 ----------- >72x/72+90y/72 >= $360 /72---- >x+1.25y >= $5

y >= (5-x)/1.25--------------see the graph in attached figure 

 

case A---------- > (5,2) (3,3)  (1,4)

72x+90y --------- > 72*5+90*2=540 >= 360----- > is solution

72x+90y --------- > 72*3+90*3=486 >= 360----- > is solution

72x+90y --------- > 72*1+90*4=432 >= 360----- > is solution

 

case B------------ >  (4,0) (2,2)  (1,1)

72x+90y --------- > 72*4+90*0=288 < 360----- > is not solution

72x+90y --------- > 72*2+90*2=324 < 360----- > is not solution

72x+90y --------- > 72*1+90*1=162 < 360----- > is not solution

 

case C------------ >  (3,1) (2,2)  (1,0)

72x+90y --------- > 72*3+90*1=306 < 360----- > is not solution

72x+90y --------- > 72*2+90*2=324 < 360----- > is not solution

72x+90y --------- > 72*1+90*0=72 < 360----- > is not solution

 

case D------------ >  (4,0) (3,3)  (1,4)

72x+90y --------- > 72*4+90*0=288 < 360----- > is not solution

72x+90y --------- > 72*3+90*3=486 >= 360----- > is solution

72x+90y --------- > 72*1+90*4=432 >= 360----- > is solution

 

<span>the answer is case A </span>



You might be interested in
What is the decimal equivalent of the fraction?
Anton [14]
7 divided by 12 = 0.583
7 0
3 years ago
Read 2 more answers
Penny sells knitted scarves for 12$ each. The cost of supplies to make each scarf is x dollars. How much profit will Penny make
vodomira [7]

Answer:

If I'm guessing, you're supposed to write an equation. So the answer would be yx + 12y.

Step-by-step explanation:

4 0
3 years ago
Find a vector of magnitude 3 in the direction of v = 10i - 24k. The vector is Oi-Oj+k (Simplify your answer. Use integers or fra
Soloha48 [4]

Given :

A vector v = 10i - 24k.

To Find :

A vector of magnitude 3 in the direction of v = 10i - 24k.

Solution :

Unit vector in the direction  of vector v is :

\^{v}=\dfrac{v}{|v|}\\\\\^{v}=\dfrac{10i-24k}{\sqrt{10^2+24^2}}\\\\\^{v}=\dfrac{10i-24k}{26}

Now , vector of magnitude 3 in direction v is :

r=3 \^{v}\\\\r=3\times \dfrac{ (10i-24k)}{26}\\\\r=\dfrac{3}{13} (5i-12k)

Hence , this is the required solution .

6 0
2 years ago
#9 and #10<br> Please show work
Tatiana [17]

Answer:

Part 9) The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13

Part 10) The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot

Step-by-step explanation:

Part 9)

Let

x ----> number of items on Emily's grocery list

x ----> number of items on Bobby's grocery list

we know that

y=2x+3 ----> equation A

x=y-8 ----> equation B

Solve by substitution

Substitute equation A in equation B

x=(2x+3)-8

solve for x

x=2x-5

2x-x=5

x=5

Find the value of y

y=2(5)+3=13

therefore

The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13

Part 10)

Let

x ----> the height of the taller bookshelf in feet

y ----> the height of the shorter bookshelf in feet

we have

x=5y-1 ----> equation A

Remember that

1\ ft=12\ in

To convert inches to feet divide by 12

so

60\ in=60/12=5\ ft

x+y=5 ----> equation B

Solve the system by substitution

substitute equation A in equation B

(5y-1)+y=5

solve for y

5y+y=5+1

6y=6

y=1\ ft

Find the value of x

x=5(1)-1=4\ ft

therefore

The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot

3 0
3 years ago
What is the slope of 3x-4y=3
aleksley [76]
Let's solve for x.<span><span><span>3x</span>−<span>4y</span></span>=3</span>Step 1: Add 4y to both sides.<span><span><span><span>3x</span>−<span>4y</span></span>+<span>4y</span></span>=<span>3+<span>4y</span></span></span><span><span>3x</span>=<span><span>4y</span>+3</span></span>Step 2: Divide both sides by 3.<span><span><span>3x</span>3</span>=<span><span><span>4y</span>+3</span>3</span></span><span>x=<span><span><span>43</span>y</span>+1</span></span>Answer:<span>x=<span><span><span>43</span>y</span>+<span>1</span></span></span>
7 0
3 years ago
Other questions:
  • Vertical angles are opposite angles with the same vertex <br> true or false
    13·1 answer
  • I will give BRAINLIEST
    11·1 answer
  • Which of the following equations is equivalent to y-3x=4 ?
    7·1 answer
  • Help me solve this problem pleaseeeeee
    9·1 answer
  • 6 - 2x = 6x = 10 + 6
    11·2 answers
  • HELP ASAP WILL MARK BRAINLIEST IF RIGHT!
    9·1 answer
  • paulette has arrived at cape horn. there are five penguins waiting to cross over to antarctica. jim goes before john but after j
    10·1 answer
  • Help me lollllllllll!!!!!
    15·1 answer
  • 8: Harry is 3 years older and Andy is twice as old as
    15·2 answers
  • Select the correct answer from each drop-down menu.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!