Which of the following can be represented by the equation 3x = 24 ?(1 point)

Question

Responses

The cost of a pair of shoes is three times the cost of a shirt. If the cost of the shirt is $24, how much does the pair of shoes cost?
The cost of a pair of shoes is three times the cost of a shirt. If the cost of the shirt is $24, how much does the pair of shoes cost?

Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?
Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?

Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?
Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?

A survey was conducted to determine the favorite subject of seventh grade students. One-third of all surveyed, or 24 students, said math is their favorite subject. How many students were surveyed?

Answer 1

To determine which scenario can be represented by the equation \(3x = 24\), we need to analyze each option based on how they relate to the equation.

1. The cost of a pair of shoes is three times the cost of a shirt. If the cost of the shirt is $24, how much does the pair of shoes cost?

   • This cannot be represented by \(3x = 24\) because it would imply \(x\) (the cost of the shirt) is $24, and \(3 \times 24\) gives $72 for the shoes, not solving for \(x\).

2. Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?

   • This also does not fit \(3x = 24\) because if \(x\) is how many stickers each received (24), the total \( = 3(24) = 72\), which does not solve for \(x\).

3. Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?

   • Here, \(x\) would be the number of weeks. Since he picks 3 words per week, this can be expressed as \(3x = 24\) (3 words per week multiplied by \(x\) weeks = total 24 words).

4. A survey was conducted to determine the favorite subject of seventh-grade students. One-third of all surveyed, or 24 students, said math is their favorite subject. How many students were surveyed?

   • This can be represented as \(\frac{1}{3} \text{ of total surveyed} = 24\), which does not match the form of \(3x = 24\).

The correct response that can be represented by the equation \(3x = 24\) is:

Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?

Answer 2

The temperature dropped by 12° in 5 hours. The temperature dropped the same amount every hour. Complete the equation that represents the amount of change, x , of temperature every hour and solve this equation.(1 point)
5x= _____

The temperature decreased by____ ° every hour.

Answer 3

To find the equation that represents the amount of change in temperature, \(x\), every hour, we start with the total temperature drop of 12° over 5 hours.

Since the temperature dropped the same amount every hour, we can set up the equation:

\[5x = 12\]

Now, we solve for \(x\):

1. Divide both sides of the equation by 5: \[ x = \frac{12}{5} = 2.4 \]

Thus, we can complete the equation and state the hourly temperature decrease:

Complete the equation: \[5x = 12\]

The temperature decreased by 2.4° every hour.

Answer 4

Which of the following equations has a solution of −7?(1 point)
Responses

4x−23=5 
4 x minus 23 equals 5

−x+3=−4 
negative x plus 3 equals negative 4

5x+11=−24 
5 x plus 11 equals negative 24

−3x−8=−29 

Answer 5

To determine which of the given equations has a solution of \(-7\), we will substitute \(-7\) for \(x\) in each equation and check if the equations hold true.

1. Equation: \(4x - 23 = 5\)

   • Substitute \(x = -7\): \[ 4(-7) - 23 = 5 \ -28 - 23 = 5 \ -51 \neq 5 \quad \text{(not a solution)} \]

2. Equation: \(-x + 3 = -4\)

   • Substitute \(x = -7\): \[ -(-7) + 3 = -4 \ 7 + 3 = -4 \ 10 \neq -4 \quad \text{(not a solution)} \]

3. Equation: \(5x + 11 = -24\)

   • Substitute \(x = -7\): \[ 5(-7) + 11 = -24 \ -35 + 11 = -24 \ -24 = -24 \quad \text{(solution)} \]

4. Equation: \(-3x - 8 = -29\)

   • Substitute \(x = -7\): \[ -3(-7) - 8 = -29 \ 21 - 8 = -29 \ 13 \neq -29 \quad \text{(not a solution)} \]

The only equation that has a solution of \(-7\) is:

5x + 11 = -24

Answer 6

Which of the following equations has a solution different from the rest?  (1 point)
Responses

3/4x+5=−1/4
Start Fraction 3 over 4 End Fraction x plus 5 equals negative Start Fraction 1 over 4 End Fraction

1/2x−3=1/2
Start Fraction 1 over 2 End Fraction x minus 3 equals Start Fraction 1 over 2 End Fraction

−0.35x−0.52=1.93 
negative 0.35 x minus 0.52 equals 1.93

−1/7x−3/4=1/4

Answer 7

To find out which of the given equations has a solution that is different from the others, we'll solve each equation for \(x\) and see what the solutions are.

1. Equation: \(\frac{3}{4}x + 5 = -\frac{1}{4}\) \[ \frac{3}{4}x = -\frac{1}{4} - 5 \ \frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} \ \frac{3}{4}x = -\frac{21}{4} \ x = -\frac{21}{4} \cdot \frac{4}{3} = -7 \]

2. Equation: \(\frac{1}{2}x - 3 = \frac{1}{2}\) \[ \frac{1}{2}x = \frac{1}{2} + 3 \ \frac{1}{2}x = \frac{1}{2} + \frac{6}{2} \ \frac{1}{2}x = \frac{7}{2} \ x = \frac{7}{2} \cdot 2 = 7 \]

3. Equation: \(-0.35x - 0.52 = 1.93\) \[ -0.35x = 1.93 + 0.52 \ -0.35x = 2.45 \ x = \frac{2.45}{-0.35} \approx -7 \]

4. Equation: \(-\frac{1}{7}x - \frac{3}{4} = \frac{1}{4}\) \[ -\frac{1}{7}x = \frac{1}{4} + \frac{3}{4} \ -\frac{1}{7}x = 1 \ x = 1 \cdot -7 = -7 \]

Now, we can summarize the solutions:

1. \(\frac{3}{4}x + 5 = -\frac{1}{4} \Rightarrow x = -7\)
2. \(\frac{1}{2}x - 3 = \frac{1}{2} \Rightarrow x = 7\)
3. \(-0.35x - 0.52 = 1.93 \Rightarrow x \approx -7\)
4. \(-\frac{1}{7}x - \frac{3}{4} = \frac{1}{4} \Rightarrow x = -7\)

The equation that has a solution different from the rest is:

\(\frac{1}{2}x - 3 = \frac{1}{2}\), which gives \(x = 7\).

Answer 8

Lindsay practices the guitar 50 minutes on Saturday and 30 minutes on most weekdays. Last week she practiced 140 minutes. How many weekdays did she practice? Write an equation in the form px+q=r to represent this problem.(2 points

____x + ______ = ______

Answer 9

To represent the problem as an equation in the form \(px + q = r\), we need to define our variables and then translate the situation into an equation.

Let \(x\) be the number of weekdays Lindsay practiced the guitar.

She practices:

• 50 minutes on Saturday
• 30 minutes on each weekday

The total practice time for the weekdays can be expressed as \(30x\) (since she practices 30 minutes for each weekday she practices, and \(x\) is the number of weekdays).

The total practice time last week was 140 minutes.

We can set up the equation as follows:

\[ 30x + 50 = 140 \]

Now we can identify the components:

• \(p = 30\) (the minutes practiced each weekday),
• \(q = 50\) (the minutes practiced on Saturday),
• \(r = 140\) (the total minutes practiced in the week).

So, the equation in the form \(px + q = r\) is:

30x + 50 = 140

Answer 10

A baby elephant weighs 150 pounds when born. It gains 2 pounds per day during the first year. How many days will it take the elephant to weigh a total of 224 pounds

Answer 11

To determine how many days it will take for the baby elephant to weigh a total of 224 pounds, we can set up the problem as follows:

1. The baby elephant weighs 150 pounds at birth.
2. It gains 2 pounds per day.

We want to find out how many days it takes for the elephant's weight to reach 224 pounds.

First, we find out how much weight it needs to gain to reach 224 pounds:

\[ \text{Weight gain needed} = 224 \text{ pounds} - 150 \text{ pounds} = 74 \text{ pounds} \]

Next, since the elephant gains 2 pounds per day, we can determine the number of days needed to gain 74 pounds by dividing the total weight gain needed by the daily weight gain:

\[ \text{Days} = \frac{74 \text{ pounds}}{2 \text{ pounds/day}} = 37 \text{ days} \]

Therefore, it will take the baby elephant 37 days to weigh a total of 224 pounds.