Mixed Deck — All IAAT Topics Flashcards

The table below shows the cost for a plumbing service based on the number of hours worked. Which equation represents the relationship between the total cost (C) and the number of hours worked (h)? | Hours (h) | Total Cost (C) | |---|---| | 1 | $110 | | 2 | $170 | | 3 | $230 | | 4 | $290 |

Answer: C = 60h + 50

First, find the hourly rate by calculating the difference in cost for each additional hour: $170 - $110 = $60; $230 - $170 = $60. This means the plumber charges $60 per hour (60h). Next, determine the fixed fee. Using the first hour: C = 60(1) + fixed fee = $110. Solving for the fixed fee gives $50. Therefore, the equation is C = 60h + 50. This can be verified with another point: for h=2, C = 60(2) + 50 = 120 + 50 = $170, which matches the table.

In a class of 50 students, 23 are girls and the remaining are boys. Find the ratio of the number of boys to the number of girls.

Answer: 27:23

Explanation: Total number of students = 50; Number of girls = 23. Total number of boys = Total number of students - Total number of girls = 50 - 23 = 27 Therefore, the desired ratio is, (Number of boys: Number of girls), which is 27:23.

A community garden tracks the growth of a sunflower. The table below shows the height of the sunflower at the end of each week. If the pattern of growth continues, what will be the height of the sunflower at the end of Week 6? | Week (W) | Height (cm) | |---|---| | 1 | 15 | | 2 | 21 | | 3 | 27 | | 4 | 33 |

Answer: 45 cm

By analyzing the table, we can see that the sunflower grows by 6 cm each week (21 - 15 = 6; 27 - 21 = 6). To find the height in Week 6, continue the pattern. Week 5 height would be 33 + 6 = 39 cm. Week 6 height would be 39 + 6 = 45 cm.

A batch of paint requires blue and yellow in a 3:1 ratio. To make 40 gallons of this paint, how many gallons of yellow are needed?

Answer: 10 gallons

Total parts = 3 + 1 = 4; yellow = (1/4) × 40 = 10 gallons.

Sophia baked cookies for her class. Every student had one cookie, including Sophia. At the end of the school day, 3 cookies were left. How many kids were in the class?

Answer: n - 3

Explanation: Let's denote the total number of cookies Sophia baked as 𝑛. Since every student, including Sophia, had one cookie, and 3 cookies were left at the end of the school day, the number of cookies eaten was n − 3. This number of cookies eaten is equal to the number of kids in the class since each student had one cookie. Therefore, the number of kids in the class is represented by the expression 𝑛 − 3.

Which of the following lists of numbers is ordered from greatest to least?

Answer: 0.5, 0, -3/2, -1.5

To compare the numbers, convert them all to the same format. -3/2 is equal to -1.5. So the numbers are -1.5, -1.5, 0, and 0.5. When ordered from greatest to least, the sequence is 0.5, 0, and then -1.5. Since -3/2 and -1.5 are equal, their order doesn't matter relative to each other. The correct list is 0.5, 0, -3/2, -1.5.

Which of the following expressions represents the sum of 5 and twice x?

Answer: X + 5

Explanation: The sum of 5 and twice x is represented by the expression x + 5, as "twice x" is equivalent to 2x, and the sum of 5 and 2x is x + 5.

If 12 workers can complete a job in 8 days, how many days will 6 workers need to complete the same job?

Answer: 16 days

This is inverse proportion: 12 × 8 = 6 × d, so d = 96 ÷ 6 = 16 days.

A company sells two products, Gadgets and Widgets. The bar chart shows the number of units sold for each product in a month, and the table shows the profit per unit. Which statement is best supported by the data? [A bar chart shows 'Units Sold'. For 'Gadgets', the bar reaches 150. For 'Widgets', the bar reaches 200.] | Product | Profit per Unit | |---|---| | Gadget | $8 | | Widget | $5 |

Answer: The company made more profit from Gadgets than from Widgets.

To determine the total profit for each product, multiply the units sold by the profit per unit. Profit from Gadgets: 150 units * $8/unit = $1200. Profit from Widgets: 200 units * $5/unit = $1000. Comparing the total profits, $1200 (Gadgets) is greater than $1000 (Widgets). Therefore, the company made more profit from Gadgets.

There are 49 boys and 28 girls in a school auditorium. Express the ratio of the number of boys to that of girls.

Answer: 7:4

Explanation: Given, the number of boys = 49; and the number of girls = 28. The GCF of 49 and 28 is 7. Now, to simplify, divide the two terms by their GCF which is 7. This means, (49 ÷ 7)/(28 ÷ 7) = 7/4. Therefore, the ratio of the number of boys to that of girls = 7:4.

A recipe for a fruit smoothie requires 3 ounces of yogurt for every 5 ounces of mixed berries. Based on this relationship, which of the following tables correctly shows the amount of yogurt and berries needed for different quantities of the smoothie? [Table A shows Yogurt(oz): 6, 9, 12 and Berries(oz): 10, 15, 20. Table B shows Yogurt(oz): 6, 8, 10 and Berries(oz): 10, 13, 16. Table C shows Yogurt(oz): 5, 10, 15 and Berries(oz): 3, 6, 9. Table D shows Yogurt(oz): 6, 9, 12 and Berries(oz): 8, 11, 14.]

Answer: Table A

The problem states a ratio of 3 ounces of yogurt to 5 ounces of berries (3:5). We need to find the table where this ratio holds true for all entries. In Table A, the ratios are 6:10 (which simplifies to 3:5), 9:15 (simplifies to 3:5), and 12:20 (simplifies to 3:5). All pairs maintain the required 3:5 ratio. The other tables do not consistently follow this ratio.

The graph below shows the number of books read by students in a book club over four months. Which of the following statements is best supported by the information in the graph? [A bar graph shows 'Books Read by Book Club'. The x-axis is labeled 'Month' with bars for January, February, March, and April. The y-axis is labeled 'Number of Books' from 0 to 50 in increments of 10. January's bar reaches 25, February's reaches 35, March's reaches 30, and April's reaches 45.]

Answer: The greatest increase in the number of books read occurred between March and April.

To find the correct statement, evaluate each option. A is incorrect because reading decreased from February (35) to March (30). B is incorrect because the first two months total 25+35=60 books, while the last two months total 30+45=75 books. C is correct because the increases were: Jan-Feb (35-25=10), Feb-Mar (a decrease), and Mar-Apr (45-30=15), making the March to April increase the largest. D is incorrect because the total is 25+35+30+45=135 books, and the average is 135/4 = 33.75.

A pizza restaurant charges a flat fee of $3 for delivery and $11 for each pizza ordered. Which equation can be used to find the total cost (C) for any number of pizzas (p)?

Answer: C = 11p + 3

The total cost (C) is the sum of the cost of the pizzas and the delivery fee. The cost of the pizzas is $11 times the number of pizzas (p), which is 11p. The delivery fee is a constant $3. Therefore, the correct equation is C = 11p + 3.

Which of the following verbal statements correctly represents the algebraic expression 2(n - 5)?

Answer: Twice the difference of a number and five.

The expression (n - 5) represents 'the difference of a number and five'. The number 2 outside the parentheses indicates that this entire difference is multiplied by two, or 'twice' the difference.

Which of the following ratios is equivalent to 6:9?

Answer: 2:3

Dividing both 6 and 9 by 3 gives 2:3, which is the simplified form.

In a proportion, if a/b = c/d, which of the following must also be true?

Answer: a × d = b × c

In any proportion a/b = c/d, the cross-products are equal: a × d = b × c.

A person has 20 coins consisting of only dimes and quarters. The total value of the coins is $3.20. Which system of equations can be used to find the number of dimes (d) and quarters (q)?

Answer: d + q = 20 AND 0.10d + 0.25q = 3.20

The problem can be described by two separate relationships, leading to two equations. The first is about the quantity of coins: the number of dimes (d) plus the number of quarters (q) equals 20. This gives the equation d + q = 20. The second is about the total value: the value of the dimes (0.10d) plus the value of the quarters (0.25q) equals $3.20. This gives the equation 0.10d + 0.25q = 3.20.

The line graph below shows the temperature in a city over a 12-hour period. During which two-hour interval did the temperature increase at the highest rate? [A line graph shows 'City Temperature'. The x-axis is 'Time of Day' from 6 AM to 6 PM in 2-hour increments. The y-axis is 'Temperature (°F)' from 40 to 70. The data points are: 6 AM at 45°F, 8 AM at 50°F, 10 AM at 60°F, 12 PM at 65°F, 2 PM at 68°F, 4 PM at 67°F, 6 PM at 62°F.]

Answer: 8 AM to 10 AM

To find the highest rate of increase, look for the steepest upward slope on the graph. Calculate the temperature change for each interval: 6-8 AM: 50-45 = 5°F increase. 8-10 AM: 60-50 = 10°F increase. 12-2 PM: 68-65 = 3°F increase. 4-6 PM: 62-67 = 5°F decrease. The greatest increase was 10°F, which occurred between 8 AM and 10 AM.

A gamer starts a level with 1500 points. In the first minute, they lose 80 points. In the second minute, they find a treasure that triples their current score. In the third minute, they use a power-up that costs 250 points. What is the gamer's final score?

Answer: 4010

First, calculate the score after the first minute: 1500 - 80 = 1420. Next, triple this new score: 1420 × 3 = 4260. Finally, subtract the cost of the power-up: 4260 - 250 = 4010. The final score is 4010.

There were 46 kids in the tram, in which 26 were boys and 20 were girls. What is the ratio of the boys to the total number of girls?

Answer: 13:10

Explanation: The ratio of boys to the total number of girls is found by dividing the number of boys by the number of girls. In this case, there are 26 boys and 20 girls. So, the ratio of boys to girls is 26:20, which simplifies to 13:10.