Vicky bought 3 1/2 pounds of oranges. Each pound costs $3.90. Which of the following equations represents the total cost, c , Vicky paid for the oranges and the amount of money she spent?(1 point)

Question

Responses

3.90c=3.5; Vicky paid $0.90.
3.90 c equals 3.5 ; Vicky paid $0.90.

c/3.5=3.90; Vicky paid $13.65. 
Start Fraction c over 3.5 End Fraction equals 3.90 ; Vicky paid $13.65. 

c/3.90=3.5; Vicky paid $1.11. 
Start Fraction c over 3.90 End Fraction equals 3.5 ; Vicky paid $1.11. 

3.90/3.5=c; Vicky paid $13.65. 

Answer 1

To find the total cost \( c \) Vicky paid for the oranges, we can use the equation:

\[ c = \text{(cost per pound)} \times \text{(number of pounds)} \]

In this case, the cost per pound is $3.90 and the number of pounds is \( 3\frac{1}{2} \) or \( 3.5 \).

So, the equation becomes:

\[ c = 3.90 \times 3.5 \]

Calculating the total cost:

\[ c = 3.90 \times 3.5 = 13.65 \]

Thus, the equation that represents the total cost Vicky paid is not explicitly among the options, but one of the options represents the relationship incorrectly.

We check the responses to find the closest match:

1. \( 3.90c = 3.5 \); Vicky paid $0.90. - Incorrect
2. \( c/3.5 = 3.90 \); Vicky paid $13.65. - This is an incorrect representation of the cost calculation but gives the right total.
3. \( c/3.90 = 3.5 \); Vicky paid $1.11. - Incorrect
4. \( 3.90/3.5 = c \); Vicky paid $13.65. - incorrect setup.

The correct format should be \( c = 3.90 \times 3.5 \) or stated as \( c = 13.65 \). Since the interpretation \( c/3.5 = 3.90 \) implies that you would multiply by 3.5 to get cost, and \( 3.90 \) is the price per pound, this equation \( c = 3.90 \times 3.5 \) leads directly to \( c = 13.65 \).

The most valid option that approaches this concept (despite the incorrect structure) would be:

Option 2 (or the one closest):

\( \frac{c}{3.5} = 3.90; \) Vicky paid $13.65.

Thus, the option that gives the total Vicky paid correctly is the second one because it derives a similar relationship through the cost per pound and utilizes the amounts accordingly.

Answer 2

Is that the answer

Answer 3

I apologize for any confusion in my previous response. Let’s clarify the correct choice based on the question regarding Vicky's purchase of oranges.

Vicky bought \(3.5\) pounds of oranges at a cost of \(3.90\) per pound. The total cost \(c\) can be calculated with the equation:

\[ c = \text{(cost per pound)} \times \text{(number of pounds)} \] This means:

\[ c = 3.90 \times 3.5 \]

Calculating:

\[ c = 13.65 \]

Now analyzing the given options:

1. 3.90c = 3.5; Vicky paid $0.90. - Incorrect
2. c/3.5 = 3.90; Vicky paid $13.65. - Correct relationship regarding the calculation, because if you multiply both sides by \(3.5\), you will indeed find \(c = 3.90 \times 3.5\).
3. c/3.90 = 3.5; Vicky paid $1.11. - Incorrect
4. 3.90/3.5 = c; Vicky paid $13.65. - Incorrect format

The best match is:

Option 2: c/3.5 = 3.90; Vicky paid $13.65.

This correctly represents the relationship and provides the total paid amount. So, yes, Option 2 is the answer to the question.

Answer 4

A culture of a certain bacteria doubles every hour. At 9:00 a.m, there were already 120 bacteria. Which equation represents the number of bacteria, n , at 8:00 a.m? How many bacteria were there?(1 point)
Responses

2n=120; at 8:00 a.m., there were 60 bacteria.
2 n equals 120 ; at 8:00 a.m., there were 60 bacteria.

n/2=120; at 8:00 a.m., there were 60 bacteria.
  Start Fraction n over 2 End Fraction equals 120 ; at 8:00 a.m., there were 60 bacteria.

n/2=120; at 8:00 a.m., there were 240 bacteria.
Start Fraction n over 2 End Fraction equals 120 ; at 8:00 a.m., there were 240 bacteria.

2n=120; at 8:00 a.m., there were 240 bacteria.

Answer 5

Given that the bacteria double every hour, when we look at the number of bacteria at 9:00 a.m., which is 120, we can determine how many bacteria were present at 8:00 a.m.

Since the bacteria double every hour, the relationship between the number of bacteria at 8:00 a.m. (let's call it \(n\)) and the number of bacteria at 9:00 a.m. (120) can be expressed as:

\[ 2n = 120 \]

This equation states that if you take the number of bacteria at 8:00 a.m. and double it, you will get the number of bacteria at 9:00 a.m.

Now, to find \(n\) (the number of bacteria at 8:00 a.m.), we can solve the equation:

1. Divide both sides by 2: \[ n = \frac{120}{2} = 60 \]

This tells us that at 8:00 a.m., there were 60 bacteria.

Based on the options provided, the correct equation and interpretation are:

Option 1: 2n=120; at 8:00 a.m., there were 60 bacteria.

This answer correctly states the number of bacteria at 8:00 a.m. and uses the right equation to represent the relationship between the counts at the two times.

Answer 6

A survey is conducted in a certain neighborhood to find out residents’ favorite vacation spot. Two-fifths of the respondents, or 80 residents, said they like spending their vacation at the beach. Which equation represents the number of residents, r, surveyed? How many residents were surveyed?(1 point)
Responses

2/5r=80; 200 residents were surveyed. 
Start Fraction 2 over 5 End Fraction r equals 80 ; 200 residents were surveyed. 

2/5r=80; 32 residents were surveyed. 
  Start Fraction 2 over 5 End Fraction r equals 80 ; 32 residents were surveyed. 

5/2r=80; 200 residents were surveyed.
Start Fraction 5 over 2 End Fraction r equals 80 ; 200 residents were surveyed.

80r=25; 200 residents were surveyed.

Answer 7

To determine the total number of residents surveyed, we can use the information given: two-fifths of the respondents, or 80 residents, said they like spending their vacation at the beach.

Let \( r \) be the total number of residents surveyed. According to the information, we can represent the number of residents who like the beach as:

\[ \frac{2}{5}r = 80 \]

This equation shows that two-fifths of the total number of residents surveyed equals 80 residents.

To find \( r \):

1. Multiply both sides of the equation by \( \frac{5}{2} \) to solve for \( r \): \[ r = 80 \cdot \frac{5}{2} \] \[ r = 80 \cdot 2.5 = 200 \]

So, the total number of residents surveyed is 200.

Now, let's review the provided responses to identify the correct one:

1. ( \frac{2}{5}r = 80; 200 residents were surveyed. - Correct equation and total.
2. ( \frac{2}{5}r = 80; 32 residents were surveyed. - Incorrect total.
3. ( \frac{5}{2}r = 80; 200 residents were surveyed. - Incorrect equation.
4. ( 80r = 25; 200 residents were surveyed. - Incorrect equation.

The correct response is:

Option 1: ( \frac{2}{5}r = 80; 200 residents were surveyed.