Question

Two of the most expensive cars in the world are car A and car B. The prices of these two cars differ by more than $15,000. The price of car A is $131,745. a. Assuming that you do not know which model is more expensive, write an absolute value in equality that describes this situation. Use x for the cost of car B. b. What are the possibilities for the price of car B?

Answer 1

Answer:

Part a) $\left|x-131,745\right|=15,000$

Part b) The possibilities for the price of car B are more of $146,745 or less than $116,745

Step-by-step explanation:

Part a) write an absolute value in equality that describes this situation. Use x for the cost of car B

Let

x -----> the cost of car B

we know that

The difference between the price of car B and car A in absolute value or the difference between the price of car A and car B in absolute value must be equal to 15,000

so

The absolute value in equality will be

$\left|x-131,745\right|=15,000$

Part b) What are the possibilities for the price of car B?

Solve the absolute value

$\left|x-131,745\right|=15,000$

we know that

The absolute value have two solutions

First case (positive)

$+(x-131,745)=15,000$

Adds 131,745 both sides

$x=15,000+131,745$

$x=\ 146,745$

Second case (negative)

$-(x-131,745)=15,000$

Multiply by -1 both sides

$(x-131,745)=-15,000$

Adds 131,745 both sides

$x=-15,000+131,745$

$x=\ 116,745$

Remember that

The prices of these two cars differ by more than $15,000

therefore

The possibilities for the price of car B are more of $146,745 or less than $116,745