Let's solve each question step-by-step.
Question 1:
Cost of hamburgers: $2.75 per pound
Cost of chicken: $3.50 per pound
Money to spend: $75
Amount of hamburgers bought: 12 pounds
First, calculate the cost for the hamburgers:
Cost of hamburgers = 12 pounds * $2.75/pound = $33.00
Now, subtract that from the total amount you have:
Money left for chicken = $75 - $33 = $42
Now, set up the equation for the chicken:
Let \( x \) be the pounds of chicken.
Cost of chicken = $3.50 * \( x \)
\[ 3.50x = 42 \]
\[ x = \frac{42}{3.50} = 12 \]
Answer: 12 pounds
Question 2:
Initial height: 1,400 feet
Descent rate: 75 feet per minute
The time taken to reach the ground can be calculated by:
\[ \text{Time} = \frac{\text{Height}}{\text{Rate}} \]
\[ \text{Time} = \frac{1400 \text{ feet}}{75 \text{ feet/minute}} \]
\[ \text{Time} = 18.666... \text{ minutes} \approx 18.6 \text{ minutes} \]
Answer: 18.6 minutes
Question 3:
Let \( x \) be the cost of processing fee and \( y \) be the cost per ticket.
From the information:
- \( 5y + x = 174.45 \) (for 5 tickets)
- \( 8y + x = 271.95 \) (for 8 tickets)
Subtract equation 1 from equation 2:
\[ (8y + x) - (5y + x) = 271.95 - 174.45 \]
\[ 3y = 97.50 \]
\[ y = 32.50 \]
Substituting \( y \) back into equation 1 to find x:
\[ 5(32.50) + x = 174.45 \]
\[ 162.50 + x = 174.45 \]
\[ x = 174.45 - 162.50 = 11.95 \]
Now calculate the cost for 12 tickets:
Total cost = 12 tickets * $32.50 + $11.95 = $390.95.
Answer: $401.95
Question 4:
Let \( C \) be the cost of installation.
Weekly cost: $5 per week
Total weeks: 12
Total cost = \( 12(5) + C = 210 \)
Simplify:
\[ 60 + C = 210 \]
So,
\[ C = 210 - 60 = 150 \]
Answer: $150
Question 5:
Let \( x \) be the cost per hour to rent the boat.
From Saturday's rental:
\[ 3x = 435 \Rightarrow x = \frac{435}{3} = 145 \]
From Sunday’s rental:
\[ 5x = 625 \Rightarrow x = \frac{625}{5} = 125 \]
We notice different prices, let's do linear interpolation to find the consistent hour-to-hour cost:
\[ y = mx + b \]
Through simultaneous equations (finding the slope):
For 3 hours rent costing $435:
\[ m = (625-435)/(5-3) = 190/2 = 95 \text{ per hour} \]
Cost for 2 hours:
\[ 2(95) = 190 \]
Answer: none of the choices directly match. Formula method indicates the cost might need adjustment under consideration.
If you are looking for the cost for 2 hours based on consistent cost per hour from the two sets of information, it seems there might be a variation leading to two hours costing either $285 (outlier based on $145 estimations). But nearest logical answer overall would guide you based on previous hourly confirmations. Please verify if exploring consistent data suggests specific rounding or estimation necessary here.
Overall Tracking:
- Question 1: 12 pounds
- Question 2: 18.6 minutes
- Question 3: $401.95
- Question 4: $150
- Question 5: costs may vary leading consistency needing more data to affirm choosing between suggested variants.
Ensure you review provided options accordingly.
1 answer