Henry spends the day at a ski resort. The total trip riding up the main chair lift and skiing down his favorite trail takes 40 to 50 minutes, depending on whether Henry takes a rest along the trail. He gets on the first chair lift at 8:00 am, he takes a onehour lunch break from noon to one, and he is back at the base at 4:00 pm. What is the most reasonable number of round trips Henry made during this time period?
A 6 round trips
B 7 round trips
C 9 round trips
D 11 round trips
2 Which of the following situations can be represented by the equation
p — (p x 0.30) — (p x 0.10) = 300?
A Selena is buying a desk for her office. After
receiving a 30% clearance discount and paying
a 10% tax, she pays $300 for the desk. How
much did the desk originally cost?
C Richie is buying a model airplane. The original
cost is p dollars, but it is on clearance for 30%
off. Richie also receives an additional 10% off the
original price for being a store employee. What
was the plane’s original price if Richie paid $300,
excluding tax?
B Wendy is buying a futon for her guest room.
She does not want to miss a 30% off sale so
she will pay an extra 10% of the original price
to place the futon on layaway. If Wendy pays a
total of $300, what was the original price of the
futon?
D Alex receives a 30% commission on whatever
clothing he sells in addition to his regular wage.
After deducting 10% of his earnings for income
tax, Alex’s paycheck was $300. What is the value
of p, the clothing that Alex sold?
3 Which of the following category of shapes consists of only regular quadrilaterals?
A rectangles
B triangles
C parallelograms
D squares
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I have answers for them but I don't know if they are correct. Not to be disrespectful but excuse me you are the only good tutor and only tutor I know.
1. b
2. c
3. d
Here are my answers
1. To find the most reasonable number of round trips Henry made during the given time period, let's break down the time he spent on each activity.
- He gets on the first chair lift at 8:00 am and is back at the base at 4:00 pm. This gives him a total of 8 hours for the entire day.
- He takes a one-hour lunch break from noon to one, so we subtract 1 hour from the total time, leaving us with 7 hours.
The given information states that the total trip riding up the main chair lift and skiing down his favorite trail takes 40 to 50 minutes, depending on whether Henry takes a rest along the trail. Let's assume Henry's round trip time is 50 minutes (the maximum time).
- Each round trip takes 50 minutes, which means Henry can make (60 minutes / 50 minutes) = 1.2 round trips per hour.
- Multiplying this by the number of hours (7), we get 1.2 x 7 = 8.4 round trips.
Since Henry cannot have a fraction of a round trip, we need to round down to the nearest whole number, which is 8. Therefore, the most reasonable number of round trips Henry made during this time period is 8.
Answer: None of the given options (as the closest option is 9).
2. To determine which situation can be represented by the equation p - (p x 0.30) - (p x 0.10) = 300, we need to analyze the equation and match it to the situation.
Let's break down the equation:
- p represents the original cost of an item.
- (p x 0.30) represents the 30% clearance discount, subtracted from the original cost.
- (p x 0.10) represents the 10% tax, subtracted from the discounted price.
- 300 represents the final price paid for the item.
Looking at the given situations:
- Situation A mentions Selena buying a desk for her office, after receiving a 30% clearance discount and paying a 10% tax, she pays $300 for the desk. This matches the equation p - (p x 0.30) - (p x 0.10) = 300. The desk's original cost is being calculated here.
Therefore, the situation represented by the equation is:
A) Selena is buying a desk for her office. After receiving a 30% clearance discount and paying a 10% tax, she pays $300 for the desk. How much did the desk originally cost?
3. Regular quadrilaterals are quadrilaterals with all sides and angles equal. Let's analyze each option to see which ones consist of only regular quadrilaterals:
- Option A: Rectangles have opposite sides equal in length but not necessarily all angles equal, so this option does not consist of only regular quadrilaterals.
- Option B: Triangles are not quadrilaterals, so this option does not consist of only regular quadrilaterals.
- Option C: Parallelograms have opposite sides parallel but not necessarily all angles equal, so this option does not consist of only regular quadrilaterals.
- Option D: Squares have all sides and angles equal, so this option consists of only regular quadrilaterals.
Therefore, the category of shapes that consists of only regular quadrilaterals is:
D) Squares