First, find the price per shirt at each store. Store 1: $40 / 3 shirts ≈ $13.33/shirt. Store 2: $65 / 5 shirts = $13.00/shirt. Store 2 has the better price. Now, calculate the total cost for 30 shirts from each store. Store 1: Buying 30 shirts is like buying 10 sets of 3 shirts. Cost = 10 * $40 = $400. Store 2: Buying 30 shirts is like buying 6 sets of 5 shirts. Cost = 6 * $65 = $390. The savings is the difference between the two total costs: $400 - $390 = $20.

We are given Red:Blue = 3:4 and Blue:Green = 5:2. To find the ratio of Red:Green, we need to make the 'Blue' term the same in both ratios. The least common multiple of 4 and 5 is 20. Convert the first ratio by multiplying by 5: Red:Blue = (35):(45) = 15:20. Convert the second ratio by multiplying by 4: Blue:Green = (54):(24) = 20:8. Now that the Blue term is 20 in both, we can combine them: Red:Blue:Green = 15:20:8. The ratio of red to green is 15:8.

The ratio of an object's height to its shadow's length is constant at the same time of day. Let H be the height of the pole. Set up the proportion: (person's height / person's shadow) = (pole's height / pole's shadow). So, 6/9 = H/42. Simplify the ratio 6/9 to 2/3. Now, 2/3 = H/42. Cross-multiply: 3H = 2 * 42 = 84. Divide by 3: H = 28 feet.

First, determine how much more the plant needs to grow: 30 cm - 12 cm = 18 cm. Next, set up a proportion to find the number of days, d, required for this growth: (5 cm / 8 days) = (18 cm / d days). Cross-multiply: 5d = 8 * 18 = 144. Solve for d: d = 144 / 5 = 28.8 days. Since the question asks for the number of full days it will take to be at least 30 cm tall, we must round up to the next whole day. After 28 days, it will not have reached the required height. Therefore, it will take 29 full days.

Calculate the time for Column A: Time = Distance / Speed = 250 miles / 60 mph = 25/6 hours. 25/6 = 4 and 1/6 hours. 1/6 of an hour is (1/6)*60 = 10 minutes. So, Column A is 4 hours and 10 minutes. Calculate the time for Column B: Time = Distance / Speed = 220 miles / 50 mph = 22/5 hours. 22/5 = 4 and 2/5 hours. 2/5 of an hour is (2/5)*60 = 24 minutes. So, Column B is 4 hours and 24 minutes. Since 4 hours and 24 minutes is longer than 4 hours and 10 minutes, the quantity in Column B is greater.

First, find the car's fuel efficiency in miles per gallon: 165 miles / 5 gallons = 33 miles per gallon. Then, divide the new distance by the fuel efficiency to find the gallons needed: 396 miles / 33 miles per gallon = 12 gallons. Alternatively, set up a proportion: (165 miles / 5 gallons) = (396 miles / x gallons). Cross-multiply: 165x = 396 * 5, which is 165x = 1980. Divide by 165: x = 12.

This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving a scale model width from real width, requiring identification of the correct proportional relationship. Choice A is correct because it accurately applies the proportional relationship by dividing 7 / 10 = 0.7 feet for the model. Choice C is incorrect because it results from multiplying instead, like 7 × 10 = 70 feet. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.

This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving scaling strawberries in a recipe for more servings, requiring identification of the correct proportional relationship. Choice A is correct because it accurately applies the proportional relationship by finding 20 / 8 = 2.5 per serving, then 2.5 × 12 = 30 strawberries. Choice B is incorrect because it results from adding instead of proportioning, like 20 + 5 or similar, yielding 25. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.

This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving time for a train to travel a certain distance, requiring identification of the correct proportional relationship. Choice B is correct because it accurately applies the proportional relationship by finding the rate 90 / 2 = 45 mph, then 225 / 45 = 5 hours. Choice C is incorrect because it results from misapplying the proportion, like 90 / 225 × 2, yielding about 0.8 but rounded wrong to 6. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.

This question tests middle school quantitative reasoning skills related to solving proportional relationships. Proportional relationships involve comparing two ratios or rates and finding a missing value, often using cross-multiplication or setting up equivalent fractions. In this scenario, you are asked to solve a problem involving currency exchange from dollars to euros, requiring identification of the correct proportional relationship. Choice A is correct because it accurately applies the proportional relationship by multiplying 50 × 0.80 = 40 euros. Choice B is incorrect because it results from inverting the rate, like 50 / 0.80 = 62.5 euros. To help students, teach them to set up ratios correctly and cross-multiply to find the unknown. Practice identifying key words that signal a proportional relationship, and watch for common errors like flipping ratios or miscalculating units.