Kendra’s age is half the age of Justin. Kendra is 13 years old. Which of the following equations represents Justin’s age, a 𝑎 ?(1 point) Responses 13a = 2 13 𝑎 = 2 13 a equals 2 a + 1/2 = 13 𝑎 + 1 2 = 13 a plus Start Fraction 1 over 2 End Fraction equals 13 1/2a = 13 1 2 𝑎 = 13 Start Fraction 1 over 2 End Fraction a equals 13 2a = 13

Answer 1

To represent Justin's age (a) based on the information given, we know that Kendra's age is half of Justin's age. Since Kendra is 13 years old, we can set up the equation as follows:

Kendra's Age = 0.5 × Justin's Age
13 = 0.5a

To express this in a simpler form, we can multiply both sides of the equation by 2 to eliminate the fraction:

2 × 13 = a
26 = a

Therefore, the correct equation representing Justin's age is:

a = 26

However, looking through the options you provided, it appears that the closest equivalent option would be:

2a = 26 (or, by dividing both sides by 2, you can interpret this in the same way as the solution above).

If the goal is to precisely match existing options rather than deriving a new equation, none of the other options you provided represent Justin's age accurately.

Answer 2

choose one of the responses

Answer 3

The correct response that represents Justin’s age is:

2a = 26

Since this equation can be solved to find Justin's age (which is 26 when Kendra is 13). However, if that specific option isn't present in your list, I apologize for that limitation.

Given the options you originally provided, none accurately represent her age in a straightforward way. Could you please clarify if there are more options?

Answer 4

Cooper will volunteer at a community food bank for two weeks. He will work 3.5 hours every day. Which equation represents the total number of hours, h
ℎ
, Cooper will volunteer at the community food bank? (1 point)
Responses

h/2 = 3.5
ℎ
2

=

3.5
Start Fraction h over 2 End Fraction equals 3.5

h/3.5 = 2
ℎ
3.5

=

2
Start Fraction h over 3.5 End Fraction equals 2

3.5h = 14
3.5
ℎ

=

14
3.5 h equals 14

h/14 = 3.5

Answer 5

To calculate the total number of hours, \( h \), that Cooper will volunteer at the community food bank for two weeks, we can set up the following equation:

1. Cooper works 3.5 hours every day.
2. There are 14 days in 2 weeks.

So the total hours \( h \) he will volunteer can be calculated as:

\[ h = 3.5 , \text{hours/day} \times 14 , \text{days} \]

This simplifies to:

\[ h = 3.5 \times 14 \]

Thus, the equation that represents the total number of hours \( h \) is:

\[ h = 3.5 \times 14 \]

From the responses you provided, the option that correctly represents this scenario is:

3.5h = 14 (but this represents a different context).

Based on the context of the problem, the form you are looking for should ideally be:

h = 3.5 × 14.

However, since that's not present, the closest option is:

3.5h = 14, but that is not representing the total hours correctly according to the context you've provided.

So, while none of the options correctly reflect what was stated in the problem, 3.5h = 14 is indeed the most relevant answer based on the options given. Please clarify if that’s acceptable or if you need more information!

Answer 6

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

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

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

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

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

Answer 7

To find the total cost \( c \) of the oranges that Vicky bought, you can use the following information:

• Vicky bought \( 3 \frac{1}{2} \) pounds of oranges, which is equal to \( 3.5 \) pounds.
• Each pound costs \( $3.90 \).

The total cost can be calculated using the equation:

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

So that translates into:

\[ c = 3.90 \times 3.5 \]

Now looking at the options given:

1. 3.90/3.5 = c; Vicky paid $13.65. (This is incorrect since it divides instead of multiplying)
2. c/3.90 = 3.5; Vicky paid $1.11. (This is incorrect as well)
3. c/3.5 = 3.90; Vicky paid $13.65. (This is incorrect; it should actually be \( c = 3.5 \times 3.90 \))
4. 3.90c = 3.5; Vicky paid $0.90. (This is incorrect because it doesn’t reflect the proper relationship)

None of the provided options correctly represents the equation for the total cost. However, if we were to rearrange what we already established, \( c = 3.90 \times 3.5 \), if written in terms of the given options, it would be:

c = 3.90 × 3.5, but again, this is not in your list.

If you must choose from the given options, you could clarify the numbers you're given, as the equations do not accurately represent the relationship needed to find the total cost of the oranges. If option 3 were written as \( c = 3.5 \times 3.90 \), it would be correct.

Given that none are appropriate, it seems like there might be a misalignment in the response options. If I had to pick the closest one, it would be:

c/3.5 = 3.90 (the rearranged version leads to the correct answer when re-calculating).

However, you will need to note the confusion and misrepresentation in the relationship.

Answer 8

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
𝑛
, at 8:00 a.m? How many bacteria were there?(1 point)
Responses

n/2=120
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.

n/2=120
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.

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

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

Answer 9

To find the number of bacteria at 8:00 a.m. when the bacteria double every hour, we can set up the problem based on the information provided:

• At 9:00 a.m., there are already 120 bacteria.
• Since the bacteria double every hour, the number of bacteria at 8:00 a.m. would be half of what it is at 9:00 a.m.

We can use the equation: \[ n = 2 \times 120 \] or equivalently: \[ \frac{n}{2} = 120 \]

This means that the correct equation to represent the number of bacteria at 8:00 a.m. is: \[ n/2 = 120 \]

Now, solving for \( n \): \[ n = 120 \times 2 = 240 \]

So, at 8:00 a.m., there were 240 bacteria.

From the responses you provided, the correct choice is:

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

Answer 10

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
𝑟
, surveyed? How many residents were surveyed?(1 point)
Responses

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

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

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

5/2r=80
5
2
𝑟
=
80
; 200 residents were surveyed.

Answer 11

To find the total number of residents surveyed, let’s set up the equation based on the information provided:

We know from the problem statement that two-fifths of the residents \( r \) equals 80 residents. This can be represented by the equation:

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

Now, to find \( r \), we can solve for it by multiplying both sides by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \):

\[ r = 80 \times \frac{5}{2} \] \[ r = 80 \times 2.5 \] \[ r = 200 \]

Therefore, the total number of residents surveyed is 200.

From the responses you provided, the correct choice is:

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