This is a mixture problem testing weighted average setup. Choice C (80 mL) is correct — let x = mL of Solution A. Set up the equation: acid contributed by A + acid contributed by B = acid in the final mixture: 0.20x + 0.50(40) = 0.30(x + 40). Simplify: 0.20x + 20 = 0.30x + 12. Solve: 8 = 0.10x → x = 80 mL. Choice A (40 mL) assumes equal volumes of both solutions, which would produce a 35% mixture (the average of 20% and 50%), not 30%. Choice B (60 mL) results from a setup or arithmetic error, possibly not distributing 0.30 across the full total volume on the right side. Choice D (100 mL) results from a sign or distribution error in solving the equation, perhaps writing 0.30(40) instead of 0.30(x + 40) for the right side. Pro tip: The mixture equation template is: %(A) × vol(A) + %(B) × vol(B) = %(mixture) × total volume. Always express the total volume as (vol A + vol B), and use the target percentage on the full mixture — not just one component.

The correct answer is C (220). Set up the equation: base fee + per-mile charge = total cost → 30 + 0.15m = 63 → 0.15m = 33 → m = 33 ÷ 0.15 = 220 miles. A (120) likely results from an arithmetic error when dividing 33 by 0.15, possibly misplacing a decimal. B (180) is another arithmetic error in the division. D (310) could result from failing to subtract the base fee, using the full $63 as the variable amount, then dividing incorrectly. The key step is subtracting the flat fee before dividing by the per-unit rate.

This is a Greatest Common Factor (GCF) question embedded in a real-world context. Choice D (21) is correct — the GCF determines the maximum number of identical bags with no items left over. Factor both numbers: 42 = 2 × 3 × 7 and 63 = 3² × 7. GCF = 3 × 7 = 21. Check: 42 ÷ 21 = 2 pencils per bag; 63 ÷ 21 = 3 stickers per bag. No remainder either way. Choice A (3) identifies a common factor (3 divides both 42 and 63) but not the greatest one. Choice B (7) identifies another common factor but also not the greatest. Choice C (14) = 42 ÷ 3, which is not a factor of 63 (63 ÷ 14 = 4.5). Pro tip: "Greatest number of identical groups with nothing left over" always means GCF. List prime factors of both numbers and multiply all shared prime factors together. The GCF of 42 and 63 is not their product (2,646) divided by anything — it's the product of their shared factors only.

We need to find how many groups of 4 can be formed from 28 students. This requires division: number of groups = total students ÷ students per group. So we calculate 28 ÷ 4 = 7 groups. Choice D (112) incorrectly multiplies 28 × 4 instead of dividing.

We need to find how long it takes to travel 150 miles at 60 miles per hour. Since distance = rate × time, we can rearrange to get time = distance ÷ rate. This gives us time = 150 miles ÷ 60 miles/hour = 2.5 hours. Choice B (90 hours) incorrectly subtracts instead of dividing the values.

We need to find the total rideshare cost for an 8-mile trip with a $4.50 base fee plus $1.75 per mile. The total cost equals the base fee plus the per-mile charge: total = $4.50 + ($1.75 × 8 miles). First calculate the mileage cost: $1.75 × 8 = $14.00, then add the base fee: $14.00 + $4.50 = $18.50. Choice A ($14.00) is just the mileage cost without the base fee.

We need to find how long it takes to drain 45 liters at a rate of 3 liters per minute. Time equals the total amount divided by the rate: time = 45 liters ÷ 3 liters/minute. This gives us 45 ÷ 3 = 15 minutes to drain the tank. Choice D (135 minutes) incorrectly multiplies 45 × 3 instead of dividing.

We need to find the total sugar needed for 6 batches when each batch uses 3/4 cup. To find the total, multiply the amount per batch by the number of batches: total sugar = 3/4 × 6. This equals 18/4 = 4 2/4 = 4 1/2 cups. Choice A (9/4) shows the improper fraction form before simplifying to the mixed number.

We need to find an expression for the total cost of 9 bags of mulch at $4.75 per bag plus $6 for gloves. The cost of mulch is $9 \times 4.75$, and we add the separate cost of gloves: Total = $9(4.75) + 6$. Choice A incorrectly includes the glove cost in the multiplication by 9.

This problem asks how far the bicycle can travel in 4 hours. We need to use the formula: distance = speed × time. Distance = 15 mph × 4 hours = 60 miles. Choice A (50 miles) might result from an arithmetic error or misreading the speed.