Estimation Sequence Flashcards

1. If Sara can read 15 pages in 10 minutes, how long will it take her to read 45 pages?

Answer: 30 minutes

Sara reads 15 pages in 10 minutes. To read 45 pages, which is three times the original amount (45 / 15 = 3), it will take her three times as long. Therefore, multiply her original reading time by three: 10 minutes * 3 = 30 minutes.

2. Restaurant customers tip their server only 8 percent for poor service. If their tip was $3.70, how much was their bill?

Answer: $46.25

Let 'x' represent the total bill. The tip of $3.70 represents 8% of the total bill. So, we can set up the equation: 0.08 * x = $3.70. To find 'x', divide the tip amount by the percentage (as a decimal): x = $3.70 / 0.08 = $46.25. Thus, their bill was $46.25.

3. Enrique weighs 5 pounds more than twice Brendan's weight. If their total weight is 225 pounds, how much does Enrique weigh?

Answer: 152 pounds

To solve this, set up two equations: E = 2B + 5 (Enrique's weight is 5 more than twice Brendan's) and E + B = 225 (their total weight). Substitute the first equation into the second to get (2B + 5) + B = 225, which simplifies to 3B + 5 = 225. Solving for Brendan's weight (B) gives 3B = 220, so B = 220/3 pounds. Then, substitute B back into the first equation to find Enrique's weight: E = 2(220/3) + 5 = 455/3 pounds, which is approximately 151.67 pounds. The closest option provided is 152 pounds.

4. What is the missing number in the sequence: 4, 6, 10, 18, ___, 66.

Answer: 34

To find the missing number, analyze the differences between consecutive terms in the sequence. The differences are 6-4=2, 10-6=4, and 18-10=8. This reveals a pattern where each difference is double the previous one. Following this pattern, the next difference should be 8 * 2 = 16. Adding this to the last known term, 18 + 16 = 34, gives the missing number. To verify, the subsequent difference would be 16 * 2 = 32, and 34 + 32 = 66, which matches the final term.

5. There are 64 fluid ounces in a 1\/2 gallon. If Nora fills a tank that holds 8 3\/4 gallons, how many ounces will she use?

Answer: 1,120 ounces

First, determine the conversion rate for one full gallon. Since there are 64 fluid ounces in 1/2 gallon, there are 64 * 2 = 128 fluid ounces in 1 full gallon. Next, convert the tank's capacity from mixed number to decimal: 8 3/4 gallons is equal to 8.75 gallons. Finally, multiply the total gallons by the ounces per gallon: 8.75 gallons * 128 ounces/gallon = 1,120 ounces.

6. Shaylee goes shopping for two types of fruit: mangoes that cost $2.00 each and coconuts that cost $4.00 each. If she buys 10 pieces of fruit and spends $30.00, how many pieces of each type of fruit did she buy?

Answer: 5 mangoes and 5 coconuts

Let 'm' be the number of mangoes and 'c' be the number of coconuts. We can set up two equations: m + c = 10 (total pieces of fruit) and 2m + 4c = 30 (total cost). From the first equation, we know m = 10 - c. Substitute this into the second equation: 2(10 - c) + 4c = 30. This simplifies to 20 - 2c + 4c = 30, or 20 + 2c = 30. Solving for 'c' gives 2c = 10, so c = 5 coconuts. Substituting c=5 back into m = 10 - c yields m = 5 mangoes.

7. Assuming Ed's Painting did not experience any major business changes, which of the following is likely to be closest to the number of houses he painted in 2005?

Answer: 31

This question requires interpreting a trend from a provided graph (not shown here). To find the likely number of houses painted in 2005, one would examine the data for previous years (e.g., 2002, 2003, 2004) to identify a pattern or trend in the number of houses painted. Based on the typical progression shown in such graphs, extrapolating the trend (e.g., a slight increase or stable number) from the preceding years would lead to an estimate of approximately 31 houses for 2005.

8. A house is 25 feet tall and a ladder is set up 35 feet away from the side of the house. Approximately how long is the ladder from the ground to the roof of the house?

Answer: 43 ft

This problem forms a right-angled triangle where the house's height and the distance the ladder is from the house are the two legs, and the ladder itself is the hypotenuse. Using the Pythagorean theorem, a² + b² = c², where 'a' is 25 feet and 'b' is 35 feet. Calculate 25² + 35² = 625 + 1225 = 1850. Therefore, the length of the ladder 'c' is the square root of 1850, which is approximately 43.01 feet. The closest answer choice is 43 feet.

9. If Louis travels on his bike at an average rate of 20 mph, how long will it take him to travel 240 miles?

Answer: 12 hours

To find the time it takes to travel a certain distance at a given average rate, use the formula Time = Distance / Rate. In this case, the distance is 240 miles and the average rate is 20 miles per hour. Dividing 240 miles by 20 mph gives 12 hours.

10. A soda company is testing a new sized can to put on the market. The new can is 6 inches in diameter and 12 inches in height. What is the volume of the can in cubic inches?

Answer: 339

The can is a cylinder, and its volume is calculated using the formula V = π * r² * h, where 'r' is the radius and 'h' is the height. Given the diameter is 6 inches, the radius 'r' is half of that, which is 3 inches. The height 'h' is 12 inches. Plugging these values into the formula: V = π * (3)² * 12 = π * 9 * 12 = 108π. Using the approximation π ≈ 3.14, the volume is approximately 108 * 3.14 = 339.12 cubic inches.