- The average of six numbers is 4. If the average of two of those numbers is 2, what is the average of the other four numbers?
- 5
- 6
- 7
- 8
A set of six numbers with an average of 4 must have a collective sum of 24. The two numbers that average 2 will add up to 4, so the remaining numbers must add up to 20. The average of these four numbers can be calculated as follows:
\(\frac{20}{4} = 5\)
- Kate got a 56 on her first math test. On her second math test, she raised her grade by 12%. What was her grade?
- 62.7
- 67.2
- 68.0
- 72.3
First, calculate 12% of 56.
\(56 \times 0.12 = 6.72\)
Then, add this value (the increase) to the original value of 56.
\(56 + 6.72 = 62.72\)
Rounding off, we get 62.7
- A skyscraper is 548 meters high. The building’s owners decide to increase its height by 3%. How high would the skyscraper be after the increase?
- 551 meters
- 555 meters
- 562 meters
- 564 meters
First, calculate 3% of 548 meters:
\(548 \text{ m} \times 0.03 = 16.44 \text{ m}\)
Then, add it to the original height.
\(548 \text{ m} + 16.44 \text{ m} = 564.44 \text{ m}\)
Rounding off, we get 564 meters.
- Janet makes homemade dolls. Currently, she produces 23 dolls per month. If she increased her production by 18%, how many dolls would Janet produce each month?
- 27
- 32
- 38
- 40
First, calculate 18% of 23.
\(23 \times 0.18 = 4.14\)
Then, add this value (the increase) to the original value of 23.
\(23 + 4.14 = 27.14\)
Rounding off, we get 27.
- A class contains an equal number of boys and girls. The average height of the boys is 62 inches. The average height of the all the students is 60 inches. What is the average height of the girls in the class?
- 57 inches
- 58 inches
- 59 inches
- 60 inches
Let the girls’ average height be \(g\) inches. We’re told that the overall average is 60, so we have \(\frac{62 + g}{2} = 60\) (because the two groups are the same size).
\(62 + g = 120 \Rightarrow g = 58\)
Here’s a quick way to think about this. The boys area two inches above the average. With equal group sizes, the girls must be two inches below the class average for it to balance out.
- Elijah drove 45 miles to his job in an hour and ten minutes in the morning. On the way home in the evening, however, traffic was much heavier and the same trip took an hour and a half. What was his average speed in miles per hour for the round trip?
- 30
- 45
- 33\(\frac{3}{4}\)
- 32\(\frac{1}{2}\)
First, we need to convert the two times we’re given to hours.
- Morning: \(70\text{ min} =\) \(\tfrac{70}{60}\) \(=\) \(\tfrac{7}{6}\)\(\text{ hr}\)
- Evening: \(90\text{ min} =\) \(\tfrac{90}{60}\) \(=\) \(\tfrac{3}{2}\)\(\text{ hr}\)
Then, we need to determine the total distance and time.
\(45 \text{ miles} \rightarrow \text{ round trip distance}\) \(= 45 + 45 = 90\text{ mi}\)
\(\tfrac{7}{6} + \tfrac{3}{2} = \tfrac{7}{6} + \tfrac{9}{6} = \tfrac{16}{6} = \tfrac{8}{3}\text{ hr}\)
Finally, we need to use the formula for average speed, which is \(\text{Average speed }= \text{ total distance } \div \text{ total time}\).
\(\text{Avg speed} =\) \(\dfrac{90}{\tfrac{8}{3}}\) \(= 90\) \(\cdot\) \(\tfrac{3}{8}\) \(=\) \(\tfrac{270}{8}\) \(= 33.75 = 33\)\(\tfrac{3}{4}\text{ mph}\)
- If Joey and Katrina hike an average of 3 miles per hour, about how long will it take them hike both the Beaverton Falls trail (7.25 miles) and the Copper Creek trail (4.75 miles)?
- 3 hours
- 3.5 hours
- 4 hours
- 4.5 hours
The total distance they will hike is \(7.25 \text{ mi} + 4.75 \text{ mi} = 12 \text{ mi}\). If they hike 3 miles per hour, it will take them 4 hours to hike 12 miles.
- A pasta salad was chilled in the refrigerator at 35°F overnight for 9 hours. The temperature of the pasta dish dropped from 86°F to 38°F. What was the average rate of cooling per hour?
- \(\frac{4.8°}{\text{hr}}\)
- \(\frac{5.3°}{\text{hr}}\)
- \(\frac{5.15°}{\text{hr}}\)
- \(\frac{0.532°}{\text{hr}}\)
First, calculate the total temperature drop.
\(86^\circ \text{F} – 38^\circ \text{F} = 48^\circ \text{F}\)
Given that we know the total time in the fridge (9 hours), we can use the formula \(\text{Average rate } = \text{ change } \div \text{ time}\).
\(\text{Avg rate} = \frac{-48^\circ \text{F}}{9\text{ hr}} = \frac{-16^\circ \text{F}}{3\text{ hr}} \approx \frac{-5.33^\circ\text{F}}{\text{hr}}\)
(The negative sign shows the temperature is going down.)
- Rachel spent $24.15 on vegetables. She bought 2 lb of onions, 3 lb of carrots, and 1\(\frac{1}{2}\) lb of mushrooms. If the onions cost $3.69 per lb and the carrots cost $ 4.29 per lb, what is the price per lb of mushrooms?
- $2.60
- $2.25
- $2.80
- $3.10
Begin by determining the total cost of the onions and carrots since these prices are given.
\((2 \times $3.69) + (3 \times $4.29) = $20.25\)
Next, this sum is subtracted from the total cost of the vegetables to determine the cost of the mushrooms.
\($24.15 – $20.25 = $3.90\)
Finally, the cost of the mushrooms is divided by the quantity (lb) to determine the cost per pound.
\(\text{Cost per lb }= \frac{$3}{1.5 \text{ lb}} = $2.60\)
- A roast was cooked at 325°F in the oven for 4 hours. The internal temperature rose from 32°F to 145°F. What was the average rise in temperature per hour?
- \(\frac{19.2°}{\text{hr}}\)
- \(\frac{28.3°}{\text{hr}}\)
- \(\frac{32.03°}{\text{hr}}\)
- \(\frac{37°}{\text{hr}}\)
First, calculate the total temperature rise.
\(145^{\circ}\text{F} – 32^{\circ}\text{F} = 113^{\circ}\text{F}\)
Given that the roast was in the oven for 4 hours, use the formula \(\text{Average rate } = \text{ change } \div \text{ time}\).
\(\text{Avg rate} = \frac{113^{\circ}\text{F}}{4 \text{ hr}} = \frac{28.25^{\circ}\text{F}}{\text{hr}} \approx \frac{28.3^{\circ}\text{F}}{\text{hr}}\)