Vijay needs to take a taxi, which costs a flat fee of 3 dollars, plus an additional 4 dollars per mile. If Vijay has a dollars with him, which inequality shows the number of miles, m, he can afford to travel in the taxi? Choose 1 answer: (A) 0

Question

Vijay needs to take a taxi, which costs a flat fee of 3 dollars, plus an additional 4 dollars per mile. If Vijay has  a dollars with him, which inequality shows the number of miles,  m, he can afford to travel in the taxi? Choose 1 answer: (A)  0 <= m <= 4a-3 (B)  0 <= m <= (a)/(4)-(3)/(4) (C)  4a-3 <= m (D)  (a)/(4)-(3)/(4) <= m

Bytelearn · Accepted Answer

Calculate total cost: The total cost of the taxi ride is the sum of the flat fee and the cost per mile. The flat fee is $3, and the cost per mile is $4 per mile. So, the total cost for m miles is $3 + $4m.Formulate inequality: Vijay has a dollars to spend on the taxi ride. The inequality that represents the condition that Vijay can afford the taxi ride is a ≥ 3 + 4m.Isolate variable: To find the inequality in terms of m, we need to isolate m. We do this by subtracting 3 from both sides of the inequality a - 3 ≥ 4m.Solve for m: Next, we divide both sides of the inequality by 4 to solve for m: (a - 3)/4 ≥ m.Flip inequality: Since we want the inequality to show the number of miles m he can afford, we flip the inequality to m ≤ (a - 3)/4.Consider non-negativity: We also know that m cannot be negative, so we have the additional condition that m ≥ 0. Combining this with the previous inequality, we get 0 ≤ m ≤ (a - 3)/4.Simplify inequality: Now we simplify the right side of the inequality: (a - 3)/4 = a/4 - 3/4. So the inequality becomes 0 ≤ m ≤ a/4 - 3/4.

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