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
BARSIC [14]
3 years ago
6

You have a budget of $48. You want to buy fruit and granola bars. Fruit costs $4 per pound, and the granola bars are $1 each. Yo

u need at least 10 granola bars. What combinations of fruit and granola bars can you buy?
1. Define the variables you will use in your model. (2 points)





2. Write an inequality representing the total cost of your purchase. (3 points)
a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1.





b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.





c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.





3. Write the inequality that models the number of granola bars you need to buy. (1 point)





4. Describe in words what each of your inequalities means. (2 points)
Inequality 1: ____________ means...





Inequality 2: ____________ means...





Graph the System of Inequalities
5. Graph your system of inequalities. Shade the half plane that represents the solution for each inequality, and then identify the area that represents the solution to the system of inequalities. (5 points: 1 point for each boundary line, 1 point for each correctly shaded half plane, 1 point for identifying the solution)

Interpreting the Graph
6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution. Identify the number of granola bars and pounds of fruit represented by each point, and explain why the point is or is not viable. (4 points: 1 for each point and 1 for each explanation)

Mathematics
1 answer:
zzz [600]3 years ago
3 0

1)Define the variables you will use in your model.

Let

x------->total pounds of the fruit

y-------> the total number of granola bars

TC----> total cost

Tf------> total cost of the fruit

Tg----> total cost of the granola bars

2) Write an inequality representing the total cost of your purchase. (3 points)

a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1

Tf=4*x

b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.

Tg=1*y--------> Tg=y

c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.

TC=Tf+Tg

TC=4*x+y

inequality-------> 4x+y \leq 48

3. Write the inequality that models the number of granola bars you need to buy.

You need at least 10 granola bars

so

y\geq 10

4. Describe in words what each of your inequalities means

inequality 1

4x+y \leq 48

the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars

inequality 2

y\geq 10

5. Graph your system of inequalities.

using a graph tool

see the attached figure

6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution.

Let

A-------> one point on the graph that represents a viable solution

B-------> one point on the graph that does not represent a viable solution

A(4,20)

x=4-------> total pounds of the fruit

y=20------> the total number of granola bars

check point A

substitute the values of x and y in the inequality 1

4x+y \leq 48

4*4+20\leq 48\\ 36\leq 48-------> is ok

substitute the values of x and y in the inequality 2

y\geq 10

20\geq 10--------> is ok

the point A represents a viable solution, because satisfies both inequalities

B(10,30)

x=10-------> total pounds of the fruit

y=30------> the total number of granola bars

check point B

substitute the values of x and y in the inequality 1

4x+y \leq 48

4*10+30\leq 48\\ 70\leq 48-------> is not a viable solution

substitute the values of x and y in the inequality 2

y\geq 10

30\geq 10--------> is ok

the point B is not a viable solution because does not satisfy the inequality 1

You might be interested in
Mike and John are the partners in a local bar who invest in a ratio of 7:13, respectively. They started the business with $1.5M.
Mamont248 [21]

Answer:

A) $525,000

B) $975,000

C) 35%

Step-by-step explanation:

To solve A) and B), divide the total amount of money by the sum of the parts of the ratio (7 + 13 = 20, in this case), and then multiply this by the person's portion of the ratio. This is because you are finding the worth of '1 part', and are then multiplying it to find how much money all their parts are worth together.

To solve C), take a person's portion of the ratio, divide it by the sum of the portions of the ratio and then multiply by 100% to get a percentage. In this case, 7/(7 + 13) * 100% = 7/20 * 100% = 0.35 * 100% = 35%.

7 0
3 years ago
A farmer is planning to build a right triangular enclosure in his back pasture. He has already determined the length of the base
MissTica
Plug in the other side for X Sorry if this is not helpful
8 0
3 years ago
Betty needs3/4 of a yard of fabric to make a skirt. she buys 9 yards. how many skirts can she make?
KengaRu [80]
11 skirts since you can use 3/4 on each yard of 9. Then you get a remander of 2, 3/4! 9 + 2 is 11.
3 0
3 years ago
What is the following quotient? StartFraction StartRoot 96 EndRoot Over StartRoot 8 EndRoot
steposvetlana [31]

Answer:

D 12

Step-by-step explanation:

because your just solving 96/8

3 0
3 years ago
Recall that a right triangle is a triangle with one right angle. One angle of a triangle measures 89.99°. Can the triangle be a
Anastasy [175]
Yes because the right triangle has a right angle which will equal to 90° you can place 89.99 to the nearest whole number which will give you a right angle.
7 0
3 years ago
Other questions:
  • A total of 384 tickets were sold for the school play. they were either adult tickets or student tickets. The number of student t
    9·2 answers
  • Which of these has the same answer as the problem in the box? [3 + 4 +5]
    8·2 answers
  • A hypothesis is only tentative: to make sure it's valid, you have to ___________.
    9·1 answer
  • hari borrowed rs 130000 from krishna at the rate of 21% per annum. At the end of 1 year and 6 months then how much simple intres
    8·1 answer
  • Find the area of a regular hexagon with side length 10 m. Round to the nearest tenth.​
    11·1 answer
  • What are the solutions to <br> |4b−5|=19
    10·1 answer
  • Find the ordered pair $(s,t)$ that satisfieFor a certain value of $k,$ the system \begin{align*} 3a + 4b &amp;= 7,\\ 6a + 4b &am
    15·2 answers
  • What’s 1 +1&amp;:$:&amp;!::’kejdnd
    14·1 answer
  • Find the surface area of the rectangular prism<br> 3 cm<br> 5 cm<br> 10 cm
    11·1 answer
  • Which statement about determining the quotient 12÷14 is true?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!