This question requires solving for C when T = 68 using the temperature conversion formula T = (9/5)C + 32. Substituting T = 68: 68 = (9/5)C + 32. Subtracting 32 from both sides: 36 = (9/5)C. Multiplying both sides by 5/9: C = 36 × (5/9) = 20. The key steps are isolating the variable term and then solving for C by using the reciprocal of the coefficient. A common error is incorrectly handling the fraction or making arithmetic mistakes during the solving process. When solving equations with fractions, work systematically to isolate the variable.

This question asks us to translate a word problem into an algebraic equation representing the total cost of car rental. The company charges $50 per day, so for d days the cost is 50d dollars. Additionally, they charge $0.20 per mile, so for m miles driven the cost is 0.20m dollars. The total cost C is the sum of these two components: C = 50d + 0.20m. The coefficient 2 represents the price per cupcake, and the coefficient 1 (implied) represents the price per cookie. A common error is mixing up the coefficients or incorrectly representing the unit prices in the equation. When setting up cost equations, match each coefficient with its corresponding item's unit price.

This question requires substituting x = 4 into the linear equation y = 3x + 7 to find the corresponding y-value. Substituting x = 4 gives us y = 3(4) + 7 = 12 + 7 = 19. The calculation follows the order of operations: first multiply 3 × 4 = 12, then add 7 to get 19. A common error is forgetting to multiply before adding or making arithmetic mistakes during substitution. When evaluating linear equations, substitute the given value carefully and follow order of operations precisely.

This question asks us to write an equation representing the total cost of cupcakes and cookies. Cupcakes cost $2 each, so x cupcakes cost 2x dollars. Cookies cost $1 each, so y cookies cost 1y = y dollars. The total cost is $10, giving us the equation 2x + y = 10. The coefficient 2 represents the price per cupcake, and the coefficient 1 (implied) represents the price per cookie. A common error is switching the coefficients or incorrectly representing the unit prices in the equation. When setting up cost equations, match each coefficient with its corresponding item's unit price.