Mateo rented a bike for $37. It costs $4 per hour, h, with an automatic charge of $13 to rent the bike.

Question

Which equation can be used to find out the number of hours, h, Mateo rented the bike?
(1 point)
4h + 13 = 37
4h - 13 = 37
4h - 37 = 13
4h + 37 = 13

Answer 1

To find the equation that represents the situation, we need to account for both the hourly cost and the initial rental charge. Mateo rented the bike for a total of $37, which consists of the $13 rental charge plus the cost of $4 per hour for \( h \) hours.

The correct equation can be set up as follows:

Total cost = Hourly cost + Rental charge
\( 37 = 4h + 13 \)

Rearranging this equation gives:

\( 4h + 13 = 37 \)

So, the correct answer is:

4h + 13 = 37

Answer 2

Key is the youngest of 5 siblings. Starting with the oldest sibling, each sibling was born 2 years apart. Together, the siblings are 70 years old.
Which equation can be used to determine the age, a, of Key?
(1 point)
5a - 20 = 70
20a + 5 = 70
5a + 70 = 20
5a + 20 = 70

Answer 3

To solve the problem, let's denote the ages of the 5 siblings. Since Key is the youngest, we can represent the ages of the siblings in relation to Key's age, \( a \):

• The oldest sibling's age would be \( a + 8 \) (because there are 4 siblings above Key, each 2 years older).
• The second oldest sibling's age would be \( a + 6 \).
• The third oldest sibling's age would be \( a + 4 \).
• The fourth oldest sibling's age would be \( a + 2 \).
• Key's age is simply \( a \).

Now, we can express the total age of all siblings:

\[ (a + 8) + (a + 6) + (a + 4) + (a + 2) + a = 70 \]

Simplifying this gives:

\[ 5a + 20 = 70 \]

Therefore, the correct equation to determine the age of Key is:

5a + 20 = 70

Answer 4

Key is the youngest of 5 siblings. Starting with the oldest sibling, each sibling was born 2 years apart. Together, the siblings are 70 years old.

Which equation can be used to determine the age, a, of Key?
(1 point)
5a - 20 = 70
20a + 5 = 70
5a + 70 = 20
5a + 20 = 70

Answer 5

Let’s break down the problem to determine the correct equation.

1. Define Key's Age: Let \( a \) represent the age of Key, who is the youngest.

2. Ages of the Siblings:

   • Oldest sibling: \( a + 8 \) (2 years older than the second oldest, 2 more than the third, etc.)
   • Second oldest: \( a + 6 \)
   • Third oldest: \( a + 4 \)
   • Fourth oldest: \( a + 2 \)
   • Youngest (Key): \( a \)

3. Total Age Calculation:

   • The total age of all siblings is: \[ (a + 8) + (a + 6) + (a + 4) + (a + 2) + a = 70 \]

4. Simplifying:

   • Combine like terms: \[ a + a + a + a + a + 8 + 6 + 4 + 2 = 70 \] \[ 5a + 20 = 70 \]

Thus, the equation that can be used to determine the age of Key is:

5a + 20 = 70

This matches one of the options provided.

Answer 6

The water level of a creek has risen 4.75 inches above its flood stage. It continues to rise at 2.5 inches per hour.
At this rate, how long will it take for the creek to be 12 inches above its flood stage?
(1 point)
6.7 hours
4.75 hours
2.9 hours
3.1 hours

Answer 7

To solve the problem, we need to determine how long it will take for the creek to rise from 4.75 inches above flood stage to 12 inches above flood stage.

1. Calculate the total rise needed:

   • Current rise: 4.75 inches
   • Desired rise: 12 inches
   • Therefore, the additional rise needed is: \[ 12 - 4.75 = 7.25 \text{ inches} \]

2. Rate of rise:

   • The creek is rising at a rate of 2.5 inches per hour.

3. Calculate the time:

   • We can use the formula \( \text{time} = \frac{\text{distance}}{\text{rate}} \) to find out how long it will take: \[ \text{time} = \frac{7.25 \text{ inches}}{2.5 \text{ inches/hour}} = 2.9 \text{ hours} \]

Thus, it will take 2.9 hours for the creek to be 12 inches above its flood stage.

Answer 8

The water level of a creek has risen 4.75 inches above its flood stage. It continues to rise at 2.5 inches per hour.

At this rate, how long will it take for the creek to be 12 inches above its flood stage?
(1 point)
6.7 hours
4.75 hours
2.9 hours
3.1 hours

Answer 9

To determine how long it will take for the creek to rise from 4.75 inches above flood stage to 12 inches above flood stage, follow these steps:

1. Calculate the total rise needed:

   • Current rise: 4.75 inches above flood stage
   • Desired rise: 12 inches above flood stage
   • Amount needed to rise: \[ 12 - 4.75 = 7.25 \text{ inches} \]

2. Determine the rate of rise:

   • The creek is rising at a rate of 2.5 inches per hour.

3. Calculate the time needed:

   • To find the time, use the formula: \[ \text{time} = \frac{\text{distance}}{\text{rate}} = \frac{7.25 \text{ inches}}{2.5 \text{ inches/hour}} \]
   • Perform the calculation: \[ \text{time} = \frac{7.25}{2.5} = 2.9 \text{ hours} \]

Therefore, it will take 2.9 hours for the creek to rise to 12 inches above flood stage. The correct answer is: 2.9 hours.

Answer 10

For a field trip, 4 students rode in cars, and the remaining students filled 9 buses.
How many students were in each bus if 472 students were on the trip?
(1 point)
459 students
52 students
116 students
53 students

Answer 11

To solve this problem, we first need to determine how many students rode the buses and then divide that number by the number of buses to find out how many students were in each bus.

1. Calculate the number of students who rode the buses:

   • Total students on the trip: 472
   • Students who rode in cars: 4

   Therefore, the number of students who rode the buses is: \[ 472 - 4 = 468 \text{ students} \]

2. Determine the number of students in each bus:

   • Number of buses: 9
   • Students per bus can be calculated by dividing the total number of bus riders by the number of buses: \[ \text{students per bus} = \frac{468 \text{ students}}{9 \text{ buses}} = 52 \text{ students} \]

Thus, there were 52 students in each bus. The correct answer is: 52 students.

Answer 12

For a field trip, 4 students rode in cars, and the remaining students filled 9 buses.

How many students were in each bus if 472 students were on the trip?
(1 point)
459 students
52 students
116 students
53 students

Answer 13

To find out how many students were in each bus, let's follow these steps:

1. Determine the total number of students riding buses:

   • Total students on the trip: 472
   • Students who rode in cars: 4

   So, the number of students who rode the buses is: \[ 472 - 4 = 468 \text{ students} \]

2. Calculate the number of students in each bus:

   • Number of buses: 9
   • Students per bus can be calculated as: \[ \text{students per bus} = \frac{468 \text{ students}}{9 \text{ buses}} \]

   Now, perform the calculation: \[ \text{students per bus} = 52 \text{ students} \]

Therefore, there were 52 students in each bus. The correct answer is: 52 students.

Answer 14

Kendra's savings account has a balance of $70. She puts $50 each week into her account. After a certain period of time, she has $330 in her account.
At this rate, how many weeks did it take Kendra to save $330?
(1 point)
8 weeks
4 weeks
5.2 weeks
210 weeks

Answer 15

To determine how many weeks it took Kendra to save $330, we can set up the following steps:

1. Identify the initial balance and target balance:

   • Initial balance: $70
   • Target balance: $330

2. Determine the total amount saved: \[ \text{Total amount to be saved} = \text{Target balance} - \text{Initial balance} \] \[ \text{Total amount to be saved} = 330 - 70 = 260 \]

3. Identify the amount Kendra saves each week:

   • Kendra saves $50 each week.

4. Calculate the number of weeks needed to save the total amount: \[ \text{Number of weeks} = \frac{\text{Total amount to be saved}}{\text{Amount saved per week}} \] \[ \text{Number of weeks} = \frac{260}{50} = 5.2 \text{ weeks} \]

Thus, it took Kendra 5.2 weeks to save $330. The correct answer is: 5.2 weeks.

Answer 16

Kendra's savings account has a balance of $70. She puts $50 each week into her account. After a certain period of time, she has $330 in her account.

At this rate, how many weeks did it take Kendra to save $330?
(1 point)
8 weeks
4 weeks
5.2 weeks
210 weeks

Answer 17

To determine how many weeks it took Kendra to reach a balance of $330 in her savings account, let's set up the calculation step-by-step:

1. Identify the initial balance and the target balance:

   • Initial balance: $70
   • Target balance: $330

2. Calculate the total amount needed to be saved: \[ \text{Total amount to be saved} = \text{Target balance} - \text{Initial balance} \] \[ \text{Total amount to be saved} = 330 - 70 = 260 \text{ dollars} \]

3. Identify how much Kendra saves each week:

   • Weekly savings: $50

4. Calculate the number of weeks needed to save the total amount: \[ \text{Number of weeks} = \frac{\text{Total amount to be saved}}{\text{Weekly savings}} \] \[ \text{Number of weeks} = \frac{260}{50} = 5.2 \text{ weeks} \]

Therefore, Kendra took 5.2 weeks to save $330. The correct answer is: 5.2 weeks.

Answer 18

Lyle, Katrina, and Mari have a combined age of 66 years. Their ages are three consecutive, even numbers. Let x represent the age of Lyle. Write an equation that can be used to determine the age, x, of Lyle.
(1 point)
?? + ? = ?

Answer 19

Let's define the ages of Lyle, Katrina, and Mari based on the information given:

1. Let \( x \) be the age of Lyle.
2. Since their ages are three consecutive even numbers, we can express the ages of Katrina and Mari as follows:
   • Katrina's age: \( x + 2 \) (she is the next consecutive even number)
   • Mari's age: \( x + 4 \) (she is the next consecutive even number after Katrina)

Now, we can write the equation for their combined age:

\[ x + (x + 2) + (x + 4) = 66 \]

This simplifies to:

\[ x + x + 2 + x + 4 = 66 \]

Combining like terms gives:

\[ 3x + 6 = 66 \]

Therefore, the equation that can be used to determine the age, \( x \), of Lyle is:

\[ 3x + 6 = 66 \]

So, if we express it in the format you requested, it could be:

x + (x + 2) + (x + 4) = 66

Answer 20

Andre hit 4 more home runs than twice the number of home runs Hassan hit. Together, they hit 10 home runs.
Write an equation which can be used to find the total number of home runs, h, Hassan hit.

Lyle, Katrina, and Mari have a combined age of 66 years. Their ages are three consecutive, even numbers. Let x represent the age of Lyle. Write an equation that can be used to determine the age, x, of Lyle.

(1 point)
?? + ? = ?

Answer 21

To create the equations for both scenarios given:

1. Andre and Hassan's Home Runs

Let:

• \( h \) = the number of home runs Hassan hit
• Then, Andre hit \( 2h + 4 \) home runs (4 more than twice the number Hassan hit).

Since together they hit a total of 10 home runs, we can write the equation as:

\[ h + (2h + 4) = 10 \]

This simplifies to:

\[ h + 2h + 4 = 10 \]

So, the equation we can use to find the total number of home runs \( h \) that Hassan hit can be represented by:

h + (2h + 4) = 10

---

2. Lyle, Katrina, and Mari's Ages

Let \( x \) represent Lyle's age:

• Lyle's age: \( x \)
• Katrina's age: \( x + 2 \) (next consecutive even number)
• Mari's age: \( x + 4 \) (next consecutive even number after Katrina)

Since their total age combined is 66 years, we can write the equation as:

\[ x + (x + 2) + (x + 4) = 66 \]

This simplifies to:

\[ x + x + 2 + x + 4 = 66 \]

So, the equation we can use to determine Lyle's age \( x \) can be represented by:

x + (x + 2) + (x + 4) = 66

Thus, the answers you are looking for are:

1. For Andre and Hassan's home runs:

   • h + (2h + 4) = 10

2. For Lyle, Katrina, and Mari's ages:

   • x + (x + 2) + (x + 4) = 66

Answer 22

Andre hit 4 more home runs than twice the number of home runs Hassan hit. Together, they hit 10 home runs.

Write an equation which can be used to find the total number of home runs, h, Hassan hit.

Lyle, Katrina, and Mari have a combined age of 66 years. Their ages are three consecutive, even numbers. Let x represent the age of Lyle. Write an equation that can be used to determine the age, x, of Lyle.

(1 point)
? + ? = ?

Answer 23

Sure! Let's summarize both scenarios and write the equations as requested.

1. Andre and Hassan's Home Runs:

Let \( h \) represent the number of home runs that Hassan hit. According to the problem:

• Andre hit 4 more than twice the number of home runs Hassan hit, which can be written as \( 2h + 4 \).
• Together, their total home runs is 10.

The equation would be:

\[ h + (2h + 4) = 10 \]

This can be rewritten as:

\[ h + 2h + 4 = 10 \]

So, in the format you requested, it can be expressed as:

h + (2h + 4) = 10

---

2. Lyle, Katrina, and Mari's Ages:

Let \( x \) represent Lyle's age. According to the problem:

• The ages are three consecutive even numbers:
  • Lyle’s age: \( x \)
  • Katrina’s age: \( x + 2 \)
  • Mari’s age: \( x + 4 \)

Their combined age is 66.

The equation would be:

\[ x + (x + 2) + (x + 4) = 66 \]

This can be rewritten as:

\[ x + x + 2 + x + 4 = 66 \]

So in the format you requested, it can be expressed as:

x + (x + 2) + (x + 4) = 66

---

Summary:

1. For Andre and Hassan's home runs:

   • h + (2h + 4) = 10

2. For Lyle, Katrina, and Mari's ages:

   • x + (x + 2) + (x + 4) = 66

These equations represent the relationships described in each problem!