Question

The cost of a car rental is ​$ per day plus per mile. You are on a daily budget of ​$. Write and solve an inequality to find the greatest distance you can drive each day while staying within your budget. Use pencil and paper. Find 2 other​ two-step inequalities with the same solutions. You can drive at most nothing miles per day.

Answer 1

Question:

The cost of a car rental is ​$42 per day plus 20 cents per mile. you are on a daily budget of ​$98. write and solve an inequality to find the greatest distance you can drive each day while staying within your budget. use pencil and paper. find 2 other​ two-step inequalities with the same solutions.

Answer:

(a) The greatest distance is 280 miles

(b) $30 + 0.10 m \le 58$ and $5 m-400 \le 1000$

Step-by-step explanation:

Given

$d = \ 42$ ---->daily rate

$m = 20\ cents$ -- amount per mile

$m = \ 0.20$ --- in dollars

$Budget = \ 98$

Solving (a): Inequality for the scenario

Because you are on a budget, it means that the spending can not exceed $98 (i.e. less than or equal to $98).

So, the inequality is:

$42 * days + 0.20 * miles \le Budget$

Represent days with d, miles with m and substitute 98 for Budget

$42d + 0.20m \le 98$

Because it is daily, then d = 1

$42 * 1+ 0.20 * m \le 98$

$42+ 0.20m \le 98$

Collect like terms

$0.20m \le 98 - 42$

$0.20m \le 56$

$m \le \frac{56}{0.20}$

$m \le 280$

The greatest distance is 280 miles

Solving (b): Two other inequalities with the same solution as: $m \le 280$

To do this, all you need to do is to perform the same operation on both sides of the inequality.

$m \le 280$

Multiply both sides by 0.10

$0.10 * m \le 280 * 0.10$

$0.10 m \le 28$

Add 30 to both sides

$30 + 0.10 m \le 28+30$

$30 + 0.10 m \le 58$ --- equation (1)

Another possible equation is as follows:

$m \le 280$

Multiply both sides by 5

$5 * m \le 280 * 5$

$5 m \le 1400$

Subtract 400 from both sides

$5 m-400 \le 1400-400$

$5 m-400 \le 1000$ --- equation (2)