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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

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? $\newline$ Choose $1$ answer: $\newline$ (A) $0 \leq m \leq 4 a-3$ $\newline$ (B) $0 \leq m \leq \frac{a}{4}-\frac{3}{4}$ $\newline$ (C) $4 a-3 \leq m$ $\newline$ (D) $\frac{a}{4}-\frac{3}{4} \leq m$

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Write two-variable inequalities: word problems

Full solution

Q. 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?

\newline

Choose

1

answer:

\newline

(A)

0 \leq m \leq 4 a-3

\newline

(B)

0 \leq m \leq \frac{a}{4}-\frac{3}{4}

\newline

(C)

4 a-3 \leq m

\newline

(D)

\frac{a}{4}-\frac{3}{4} \leq m

Calculate Total Cost: The total cost of the taxi ride for $m$ miles is the sum of the flat fee and the cost per mile. The flat fee is $3$ dollars and the cost per mile is $4$ dollars.
Represent Total Cost: The total cost for $m$ miles can be represented by the equation: $\text{Total Cost} = \text{Flat Fee} + (\text{Cost per Mile} \times \text{Number of Miles})$ .
Substitute Given Values: Substitute the given values into the equation: Total Cost $= 3 + 4m$ .
Set Up Inequality: Vijay can afford to take the taxi as long as the total cost is less than or equal to the amount of money he has, which is $a$ dollars. So, we have the inequality: $3 + 4m \leq a$ .
Isolate Variable: To find the inequality for $m$ , we need to isolate $m$ on one side. Subtract $3$ from both sides of the inequality: $4m \leq a - 3$ .
Solve for m: Now, divide both sides of the inequality by $4$ to solve for $m$ : $m \leq \frac{a - 3}{4}$ .
Rewrite Inequality: The inequality $m \leq \frac{a - 3}{4}$ can be rewritten as $0 \leq m \leq \frac{a - 3}{4}$ , since the number of miles cannot be negative.
Simplify Inequality: The inequality $0 \leq m \leq \frac{a - 3}{4}$ can be further simplified by dividing the numerator and the denominator by $4$ : $0 \leq m \leq \frac{a}{4} - \frac{3}{4}$ .

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