Proportionality>Applying Reasoning to Solve Ratio and Rate Problems(TEKS.Math.6.4.B)
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Texas 6th Grade Math › Proportionality>Applying Reasoning to Solve Ratio and Rate Problems(TEKS.Math.6.4.B)
A car travels 240 miles in 4 hours. At this rate, how far will it travel in 7 hours? Using proportional reasoning, what is the answer?
420 miles
360 miles
300 miles
480 miles
Explanation
Find the unit rate: $240 \div 4 = 60$ miles/hour. Predict for 7 hours: $60 \times 7 = 420$ miles. Proportion: $\frac{240}{4} = \frac{x}{7} \Rightarrow x = \frac{240\cdot 7}{4} = 420$.
A runner takes 180 steps in 2 minutes. At this rate, how many steps will the runner take in 7 minutes? Using proportional reasoning, what is the answer?
540 steps
1260 steps
630 steps
450 steps
Explanation
Unit rate: $180 \div 2 = 90$ steps/min. Prediction: $90 \times 7 = 630$ steps. Proportion: $\frac{180}{2} = \frac{x}{7} \Rightarrow x = \frac{180\cdot 7}{2} = 630$.
Printer A prints 45 pages in 3 minutes. Printer B prints 60 pages in 5 minutes. If both print for 10 minutes, how many more pages will Printer A print than Printer B? Using proportional reasoning, what is the answer?
10 pages
15 pages
40 pages
30 pages
Explanation
Rates: A is $45 \div 3 = 15$ pages/min, B is $60 \div 5 = 12$ pages/min. In 10 min: A prints $15\times 10 = 150$, B prints $12\times 10 = 120$. Difference: $150-120=30$ pages.
Twelve gallons of gas cost $38.40. At this rate, how much would 15 gallons cost? Using proportional reasoning, what is the answer?
48
41
31
45
Explanation
Unit price: $38.40 \div 12 = 3.20$ dollars/gallon. For 15 gallons: $3.20 \times 15 = 48.00$ dollars. Proportion: $\frac{38.40}{12} = \frac{x}{15} \Rightarrow x = \frac{38.40\cdot 15}{12} = 48.00$.