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2 years ago

Giuliana has 22 quarters and dollar coins worth a total of $10.75.

2 answers:

7 0

Use the letters q and d to represent # of quarters and # of dollars.

q + d = 22 coins.

$0.25q + $1.00d = $10.75 Mult. this by 100 to eliminate fractions:
25q + 100d = 1075

Subst. q = 22 - d into the 2nd equation:

25 (22 - d) + 100 d = 1075

550 - 25d + 100d = 1075
550 + 75d = 1075
75 d = 525
d = 7

q + d = 22, so if d = 7, then q = 22-7, or q=15.

There are 15 quarters and 7 dimes.

Ad libitum [116K]2 years ago

4 0

Let

q------> the number of quarters coins

d------> the number of dollars coins

we know that

$1\ quarter=\$0.25$

$q+d=22$

$q=22-d$ ------> equation A

$0.25q+d=10.75$ -----> equation B

substitute equation A in equation B

$0.25[22-d]+d=10.75$

therefore

<u>the answer is the option</u>

$0.25[22-d]+d=10.75$

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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

zzz [600]

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

$y\geq 10$

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

3 0

1 year ago

Michelle exercises for half an hour every day. How minutes in total does she exercise for over 5 days?

enyata [817]

First, Michelle exercises for thirty minutes every day.

If Michelle exercises for 30 minutes for 5 days, this would 30 × 5.

30 × 5 = 150 minutes

3 0

2 years ago

Read 2 more answers

Alchen [17]

Answer: C)27:1

Step-by-step explanation:

Given, Kent has two similar cylindrical pipes, Pipe A and Pipe B. The radius of Pipe A is 6 cm, and the radius of Pipe B is 2 cm.

Volume of cylinder = $\pi r^2h$ , where r= radius and h = height.

Also, If two figures are similar then ratio of volume is equal to the cube of any dimension .

The ratio of the volume of Pipe A to the volume of Pipe B is given by :-

$\dfrac{\text{Volume of pipe A}}{\text{Volume of pipe B}}=\dfrac{6^3}{2^3}\\\\=\dfrac{216}{8}=\dfrac{27}{1}$

Thus, the ratio of the volume of Pipe A to the volume of Pipe B = 27:1

So, the correct option is C)27:1.

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2 years ago

A rate that describes how much smaller or larger the scale drawing is than the real object

AfilCa [17]

It is called a scale factor :)

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2 years ago

A coffee shop uses two different-sized bins to store coffee beans. The volume of the smaller bin is x cubic inches and the volum

raketka [301]

Answer:

Total volume of all the bins = xS + yL

Step-by-step explanation:

Given: x cubic inches represent the volume of the smaller bin and y cubic inches represents the volume of the larger bin. The store has S smaller bins and L larger bins.

To find: an expression that represents the total volume of all the bins

Solution:

The volume of the smaller bin = x cubic inches

The volume of the larger bin = y cubic inches

Also, the store has S smaller bins and L larger bins

So,

Total volume of all the bins = xS + yL

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2 years ago