A car rental company charges a flat base fee of $30 plus $0.15 for every mile driven. If a customer's total rental cost (before taxes) is $63, how many miles did the customer drive?
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A car rental company charges a flat base fee of $30 plus $0.15 for every mile driven. If a customer's total rental cost (before taxes) is $63, how many miles did the customer drive?
A car rental company charges a flat base fee of $30 plus $0.15 for every mile driven. If a customer's total rental cost (before taxes) is $63, how many miles did the customer drive?
Explanation: 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.
A teacher is making identical gift bags with 42 pencils and 63 stickers, no items left over, same number of each item per bag. What is the greatest number of bags she can make?
Explanation: 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.
A classroom has 28 students. The teacher forms groups with 4 students in each group. How many groups can be formed?
Explanation: 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.
A train travels at a constant speed of 60 miles per hour. How long will it take the train to travel 150 miles?
Explanation: 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.
A rideshare charges a \4.50basefeeplus$1.75permile.IfJordanrides8$ miles, what is the total cost?
Explanation: We need to find the total rideshare cost for an 8-mile trip with a 4.50basefeeplus1.75 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.ChoiceA(14.00) is just the mileage cost without the base fee.
A tank contains 45 liters of water. A pump drains water at a constant rate of 3 liters per minute. How long will it take to drain the entire tank?
Explanation: 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.
A recipe uses 43 cup of sugar per batch of muffins. If Lina makes 6 batches, how much sugar does she need in total?
Explanation: 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.
A bicycle travels at 15 miles per hour. How far can it travel in 4 hours?
Explanation: 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.
A recipe requires 2 cups of flour for every 3 cups of sugar. How much flour is needed for 9 cups of sugar?
Explanation: This problem asks how much flour is needed when scaling up a recipe proportionally. The ratio is 2 cups flour for every 3 cups sugar, so we set up the proportion: 2/3 = x/9, where x is the unknown flour amount. Cross-multiplying: 3x = 2 × 9 = 18, so x = 6 cups of flour. Choice A would result from incorrectly thinking the ratio is 1:3 instead of 2:3.
A pizza is cut into 8 slices. If you eat 3 slices, what fraction of the pizza is left?
Explanation: This problem asks what fraction of the pizza remains after eating 3 slices out of 8. We need to find the remaining slices as a fraction of the whole pizza. Remaining fraction = (8 - 3) slices ÷ 8 total slices = 5/8. Choice A (1/2) might result from incorrectly calculating 4/8 instead of 5/8.