Question 6:
To find the equation that can be used to calculate the number of hours, \( x \), that Dalyn rents the boat, you need to consider the rental cost structure. The total charge is made up of a flat fee of $30 plus $10 for each hour rented.
The total charge is represented as:
\[ \text{Total charge} = \text{Flat fee} + \text{Hourly rate} \times \text{Hours} \]
So, we can write it as:
\[ 30 + 10x = 90 \]
Now, to see which option matches this equation:
A. \( 10x + 30 = 90 \) → This is correct.
B. \( 10(x + 30) = 90 \) → This is incorrect.
C. \( 30x + 10 = 90 \) → This is incorrect.
D. \( 30(x + 10) = 90 \) → This is incorrect.
The correct choice is:
A. 10x + 30 = 90; 6 hours
To find the number of hours, we can solve the equation:
\[ 10x + 30 = 90 \] \[ 10x = 90 - 30 \] \[ 10x = 60 \] \[ x = 6 \]
Question 7:
Lamont wants to have at least 50 trading cards and currently has 20. Let \( x \) represent the number of additional trading cards needed. The inequality can be formulated as:
\[ x + 20 \geq 50 \]
Now, let's solve this inequality:
\[ x + 20 \geq 50 \] \[ x \geq 50 - 20 \] \[ x \geq 30 \]
Now, let's examine the provided options:
A. \( x + 20 \geq 50 \) → True statement (this is the inequality we derived).
B. \( x + 20 \leq 50 \) → False statement.
C. \( x \geq 30 \) → True statement (this is what we derived).
D. \( x \leq 30 \) → False statement.
E. \( x \geq 70 \) → False statement.
True statements are:
A. \( x + 20 \geq 50 \) and C. \( x \geq 30 \).
1 answer