Question

Jodi bought a new car with a 14-gallon gas tank. Around town she is able to drive 336 miles on one tank of gas. On her first trip traveling on highways, she drove 448 miles on one tank of gas.
a) Write a compound inequality that represents how many miles Jodi can drive on a tank of gas. Let m represent the number of miles per gallon.
b) Rewrite the compound inequality as two simple inequalities separated by either "and" or "or".
c) Solve each simple inequality. Then write the solution in compact form.
d) Explain your solution in terms of the problem situation.
g) represent the solution on a number line. Describe the shaded region in terms of the problem situation.

Answer 1

Part A:

Answer:

$336\leq 14m\leq 448$

Step-by-step explanation:

Step 1:

Jodi bought a new car with a 14-gallon gas tank.

Around town, she can drive 336 miles on one tank of gas.

She drove 448 miles on one tank on a trip on the highway

m will represent the number of miles per gallon of gas.

Step 2:

If m represents the number of miles per gallon of gas she gets and her tank holds 14 gallons then 14m represents the number of miles she can drive.

14 gallons · $\frac{m}{1} = 14m$

Around town, she was able to drive 336 miles and on the highway, she was able to drive 448

So... $336\leq 14m\leq 48$

Part B:

Answer:

The compound inequality is two simple inequalities separated by "and" is $336\leq 14m$ and $14m < 448$.

Step-by-step explanation:

Step 1:

We are told Jodi bought a new car with a 14-gallon gas tank.

Around town, she can drive 336 miles on one tank of gas. She drove 448 miles on one tank of gas on her first trip traveling on highways

Here we need to rewrite the compound inequality

Let $m$ represent the number of miles per gallon of gas.

Step 2:

Since $14m$ must greater than or equal to $336$ and less than or equal to $448$:

The two simple inequalities must be separated by the word "and"

$336\leq 14m$ and $14m$

Part C:

Answer:

The solution of simple inequality is $24\leq m$ and $m\leq 32$

Step- by step explanation:

Step 1:

We are given Jodi bought a new car with a 14-gallon gas tank. Around town, she can drive 336 miles on one tank of gas. She drove 448 miles on one tank of gas on her first trip traveling on highways.

Step 2:

Solve each simple inequality by dividing both sides by 14:

$336\leq 14m$ and $14m\leq 448$

$\frac{336}{14}\leq \frac{14m}{14}$ and $\frac{14m}{14} \leq \frac{448}{14}$

$24\leq m$ and $m\leq 32$

Part D:

Answer:

The solution of the compound inequality is $24\leq m\leq 32$

Step 1:

We are given Jodi bought a new car with a 14-gallon gas tank. Around town, she can drive336miles on one tank of gas. She drove 448 miles on one tank of gas on her first trip traveling on highways. To solve the compound inequality without rewriting it as two simple inequalities

Step 2:

Solving compound $336\leq 14m\leq 448$ for $m$ by dividing all sides by 14

$226\leq 14m\leq 448$

$\frac{336}{14}\leq \frac{14m}{14} \leq \frac{448}{14}$

$24\leq m\leq 32$

Part G:

Answer:

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Answer 2

Let me seeee could you be more specific