Select the correct answer.
Carly tutors students in math on the weekends and offers both thirty-minute sessions and sixty-minute sessions. She earns $15 for each thirty-minute session and $25 for each sixty-minute session.
If she earned $230 this past weekend and had [tex]$x$[/tex] thirty-minute sessions and [tex]$x-2$[/tex] sixty-minute sessions, what is the value of [tex]$x$[/tex]?
A. 8
B. 6
C. 7
D. 5
Answer (2)
Set up an equation representing Carly's total earnings: 15 x + 25 ( x − 2 ) = 230 .
Simplify and solve the equation for x : 15 x + 25 x − 50 = 230 ⇒ 40 x = 280 ⇒ x = 7 .
Verify the solution: ( 15 × 7 ) + ( 25 × 5 ) = 105 + 125 = 230 .
The value of x is 7 .
Explanation
Problem Analysis Let's analyze the problem. Carly earns $15 for each thirty-minute session and $25 for each sixty-minute session. She earned $230 this past weekend. We need to find the number of thirty-minute sessions, which is represented by x , given that she had x − 2 sixty-minute sessions.
Setting up the Equation We can set up an equation to represent Carly's total earnings. The total earnings from thirty-minute sessions is 15 x , and the total earnings from sixty-minute sessions is 25 ( x − 2 ) . The sum of these earnings is equal to $230 . So, the equation is: 15 x + 25 ( x − 2 ) = 230
Solving for x Now, let's solve the equation for x :
15 x + 25 ( x − 2 ) = 230 15 x + 25 x − 50 = 230 40 x − 50 = 230 40 x = 230 + 50 40 x = 280 x = 40 280 x = 7
Verification Now we need to check if the solution makes sense. We found that x = 7 . This means Carly had 7 thirty-minute sessions and 7 − 2 = 5 sixty-minute sessions. Let's verify if this gives us the correct total earnings: ( 15 × 7 ) + ( 25 × 5 ) = 105 + 125 = 230 The total earnings match the given information, so our solution is correct.
Final Answer Therefore, the value of x is 7.
Examples
Understanding how to solve this problem can help you manage your own tutoring business or any situation where you have different rates for different services. For example, if you charge different rates for different subjects or different lengths of sessions, you can use this method to calculate your earnings and plan your schedule effectively. This also applies to other scenarios like calculating income from different types of sales or managing costs with varying prices.
Carly had 7 thirty-minute sessions, represented by x . We confirmed this by calculating her total earnings based on her rates and sessions. The chosen option is C. 7.
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