Subjects algebra

Tables Ratios 810526

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1. **Complete the table for the first set:** Given the y-value is constant at 3 for all x-values 2, 4, 6, 8, 10. 2. **Complete the table for the second set:** Given the y-value is constant at 2 for all x-values 1, 2, 3, 4, 5. 3. **Fertilizer cost problem:** a. Complete the table: - Given: 10 bags cost 140. - For 30 bags: Since 30 is 3 times 10, cost is $140 \times 3 = 420$ (not 280 as given, so we correct it). - For 40 bags: 40 is 4 times 10, cost is $140 \times 4 = 560$ (not 840 as given, so we correct it). - For 6 bags: Since 6 is 0.6 times 10, cost is $140 \times 0.6 = 84$. b. Cost for 50 bags: - 50 is 5 times 10, so cost is $140 \times 5 = 700$. 4. **Car gas usage problem:** a. Complete the table: - Given: 5 gallons for 120 miles. - For 20 gallons: 20 is 4 times 5, so distance is $120 \times 4 = 480$ miles (not 360 as given, so we correct it). b. Gallons for 600 miles: - Use ratio: $\frac{5}{120} = \frac{gallons}{600}$. - Cross multiply: $5 \times 600 = 120 \times gallons$. - Simplify: $3000 = 120 \times gallons$. - Divide both sides by 120: $$ gallons = \frac{3000}{120} $$ $$ gallons = \cancel{\frac{3000}{\cancel{120}}} = 25 $$ c. Distance for 30 gallons: - Use ratio: $\frac{5}{120} = \frac{30}{distance}$. - Cross multiply: $5 \times distance = 120 \times 30$. - Simplify: $5 \times distance = 3600$. - Divide both sides by 5: $$ distance = \frac{3600}{5} $$ $$ distance = \cancel{\frac{3600}{\cancel{5}}} = 720 $$ miles. **Final answers:** - Fertilizer cost for 50 bags is 700. - Car uses 25 gallons for 600 miles. - Car can travel 720 miles with 30 gallons.