Question

Diego and Anya live 72 miles apart. They both meet at
their favorite restaurant, which is (16x – 3) miles from
Diego's house and (5x + 2) miles from Anya's house.
Diego argues that in a straight line distance, the restaurant
is halfway between his house and Anya's house. Is Diego
right? Justify your reasoning.

Answer 1

Answer:

The restaurant is not at half way

Step-by-step explanation:

Given

$Total\ Distance = 72$

$Diego = 16x - 3$

$Anya = 5x + 2$

Required

Accept or reject Diego's claim

To do that, we need to determine the value of x by:

Diego + Anya =Total Distance

Substitute values for each parameter

$16x - 3 + 5x + 2 = 72$

Collect Like Terms

$16x + 5x = 72 + 3 - 2$

$21x = 73$

Divide both sides by 21

$x = \frac{73}{21}$

Substitute the value of x in Diego and Anya's distance

$Diego = 16x - 3$

$Diego = 16 * \frac{73}{21} - 3$

$Diego = \frac{1168}{21} - 3$

$Diego = \frac{1168 - 63}{21}$

$Diego = \frac{1105}{21}$

$Diego = 52\frac{13}{21}$

$Anya = 5x + 2$

$Anya = 5 * \frac{73}{21} + 2$

$Anya = \frac{365}{21} + 2$

$Anya = \frac{365 + 42}{21}$

$Anya = \frac{407}{21}$

$Anya = 19\frac{8}{21}$

Since, both distances are not equal,

Then Diego's claim is false and incorrect