Convert $$6\frac{1}{2}$$ hours to $$6.5$$ hours. Total earnings: $$18.50 \times 6.5 = 120.25$$. Amount spent on gas: $$\frac{2}{5} \times 120.25 = 0.4 \times 120.25 = 48.10$$. Amount saved: $$120.25 - 48.10 = 72.15$$. Choice A shows only the amount spent on gas. Choice C incorrectly calculates $$\frac{2}{5}$$ of earnings. Choice D shows total earnings before any spending.

First find the scaling factor: $$\frac{12}{8} = 1.5$$. Convert $$2\frac{1}{3}$$ to decimal: $$2.333...$$ or $$\frac{7}{3}$$. Amount needed: $$\frac{7}{3} \times 1.5 = \frac{7}{3} \times \frac{3}{2} = \frac{7}{2} = 3.5$$ pounds. Cost: $$3.5 \times 4.80 = 16.80$$. Choice A uses the original recipe amount. Choice C incorrectly calculates the scaling. Choice D makes an error in the mixed number conversion.

This problem tests solving multi-step problems with rational numbers, including whole numbers, fractions, decimals, positive and negative values, by converting between forms strategically and checking for reasonableness. Tank starts -1.8 decimal deficit, add 3 1/2 mixed=3.5 to -1.8+3.5=1.7, leak -0.6=1.7-0.6=1.1, drain 1/4 of 1.1=0.275, 1.1-0.275=0.825 L. Interprets negative as below full, adds/subtracts, multiplies fraction last. Correct multi-step tracks amount, converting mixed to decimal. Errors: ignoring negative or draining before leak. Strategy: use decimals, step-by-step, estimate -2+3.5=1.5, -0.5=1, 1/4 drain 0.25, 1-0.25=0.75 close to 0.825, check positive reasonable after add. Common mistakes: order wrong or no estimation for negative finals.

This problem involves setting up an equation based on fractional parts of an unknown total capacity. When you see a word problem about fractions of a whole where the whole is unknown, think about defining a variable for the total and translating the given information into an equation.

Let's call the total capacity $$C$$ gallons. Initially, the tank contains $$\frac{3}{4}C$$ gallons. After using $$15.5$$ gallons, the tank has $$\frac{3}{4}C - 15.5$$ gallons remaining. We're told this remaining amount equals $$\frac{1}{2}C$$ gallons (half the total capacity).

Setting up the equation: $$\frac{3}{4}C - 15.5 = \frac{1}{2}C$$

To solve, subtract $$\frac{1}{2}C$$ from both sides: $$\frac{3}{4}C - \frac{1}{2}C = 15.5$$

Converting to common denominators: $$\frac{3}{4}C - \frac{2}{4}C = 15.5$$, which gives us $$\frac{1}{4}C = 15.5$$

Therefore: $$C = 15.5 \times 4 = 62$$ gallons.

Choice A ($$60$$ gallons) might result from rounding $$15.5$$ down to $$15$$ before multiplying. Choice B ($$64$$ gallons) could come from incorrectly calculating $$16 \times 4$$ if you rounded $$15.5$$ up. Choice C ($$58$$ gallons) might occur from computational errors in the fraction arithmetic or incorrectly setting up the initial equation.

Strategy tip: In fraction word problems involving an unknown total, always define your variable clearly and translate each piece of information into mathematical expressions before setting up your equation. Double-check by substituting your answer back into the original problem.

First convert $$2\frac{3}{4}$$ to decimal: $$2.75$$ cups needed total. Maria added $$1.25$$ cups, then removed $$0.5$$ cups, leaving $$1.25 - 0.5 = 0.75$$ cups in the bowl. She still needs $$2.75 - 0.75 = 2$$ cups. Choice B incorrectly adds the removed amount instead of subtracting it. Choice C uses the original amount added without accounting for removal. Choice D represents the total needed minus only the removal amount.

Convert $$12\frac{1}{4}$$ to decimal: $$12.25$$. Starting at $$0$$, after descending $$45.8$$ m: position is $$-45.8$$. After rising $$12.25$$ m: $$-45.8 + 12.25 = -33.55$$. After descending $$8.75$$ m: $$-33.55 - 8.75 = -42.3$$. The submarine is $$42.3$$ meters below sea level. Choice A incorrectly subtracts the final descent. Choice B uses $$12.5$$ instead of $$12.25$$. Choice D makes an error in the middle calculation.

This problem combines mixed numbers, decimals, and fractions while testing your ability to scale recipes and calculate differences. When you see questions mixing different number formats, convert everything to the same form first to avoid confusion.

To find how much more nuts Maya needs, you must first determine how many nuts the scaled recipe requires. The original recipe calls for $$1\frac{1}{4}$$ cups of nuts. Converting to a decimal: $$1\frac{1}{4} = 1.25$$ cups. When Maya makes $$2.5$$ times the recipe, she needs $$1.25 \times 2.5 = 3.125$$ cups of nuts total. Since she has $$2$$ cups available, she needs $$3.125 - 2 = 1.125$$ more cups.

Choice A ($$3.125$$ cups) represents the total amount of nuts needed for the scaled recipe, not the additional amount required. This is a common trap where students stop calculating before finding the final answer. Choice B ($$0.875$$ cups) likely comes from incorrectly calculating $$2.5 - 1.25 = 1.25$$, then subtracting $$2 - 1.25 = -0.75$$, and taking the absolute value incorrectly. Choice C ($$1.25$$ cups) is simply the original amount of nuts in the recipe, showing the student forgot to scale up by $$2.5$$.

The correct answer is D ($$1.125$$ cups).

Strategy tip: In multi-step word problems, write out each calculation step clearly: (1) find the scaled requirement, (2) subtract what's available. Also, when mixing fractions and decimals, convert everything to decimals first to avoid computational errors.

Convert $$3\frac{3}{4}$$ to decimal: $$3.75$$. Starting temperature: $$-8.5°F$$. After rising $$3.75$$ degrees: $$-8.5 + 3.75 = -4.75°F$$. After dropping $$2.25$$ degrees: $$-4.75 - 2.25 = -7°F$$. Choice B incorrectly adds the drop instead of subtracting. Choice C makes an error in converting the mixed number. Choice D uses incorrect decimal conversion for the mixed number.

This problem tests solving multi-step problems with rational numbers, including whole numbers, fractions, decimals, positive and negative values, by converting between forms strategically and checking for reasonableness. In multi-step scenarios with mixed forms, such as starting with $45 whole number, subtracting $18.50 decimal, adding $30 whole, then spending 1/4 fraction of the remainder, convert fractions to decimals for easier arithmetic, like 1/4=0.25, and apply operations sequentially while tracking values step-by-step. For this specific problem, start with $45, subtract $18.50 to get $26.50, add $30 to reach $56.50, then spend $56.50 × 0.25 = $14.125 (rounds to $14.13), and subtract to find $56.50 - $14.125 = $42.375, which rounds to $42.38. The correct approach involves proper order of operations and accurate conversions, ensuring the final amount is calculated after all steps. Common errors include incorrect operation order, like multiplying before adding the deposit, or conversion mistakes such as treating 1/4 as 0.20. Strategy: read carefully to list steps, convert to decimals for consistency, execute step-by-step with running totals, estimate like 45-19+30=56, 56/4=14 spent, 56-14=42 close to $42.38, and verify reasonableness with net spending and deposit. Avoid mistakes like skipping estimation or arithmetic errors in subtraction.

This problem tests solving multi-step problems with rational numbers (whole, fraction, decimal, positive, negative), converting between forms strategically, and checking reasonableness. Multi-step with mixed forms: combine different formats (-12 whole negative, +7.5 decimal, -9/4 fraction= -2.25), apply sequentially (add 7.5, subtract 2.25). For this specific problem: -12 + 7.5 = -4.5, -4.5 - 2.25 = -6.75 m. The correct approach involves converting fraction to decimal and handling negative positions properly. Common errors include sign error (-12 +7.5 as -19.5), conversion wrong (9/4 as 2.5), or unreasonable result (positive when diving deeper). Strategy: (1) read carefully identifying all values and operations (list steps needed), (2) convert to consistent form if easier (all decimals), (3) execute step-by-step (track running total, don't skip), (4) estimate alongside (-12+8=-4, -4-2=-6 close to -6.75✓), (5) verify reasonable (ends below sea level—logical for diver), (6) check units (meters stay meters). Common mistakes: skipping estimation (missing unreasonable answers), form conversion errors, negative operations (rise is add, drop is subtract).