Tema : matemáticas OPERACIÓNES CON NÚMEROS NATURALES 1- propongan problemas que puedan resolverse a mediante de las siguientes ecuaciones

1_ 200- 5n =40- n

2_ (2a + 1)-a = 5​

165m

Question:

Artur, Olga and Wiktor participated in the race. They started from the same place at the same time and run at constant speeds. When Artur finished the race, Olga was 15 m to the finish, and Wiktor was 35 m. When Olga finished the race, Wiktor had 22 m to the finish. At what distance was the race held?

Explanation:

Let distance be x meters

Fist statement:

Artur distance = x

Olga =x-15

Wiktor = x-35

Since they are going at constant speed, time is constant for all 3.

Their speed = distance/time

x/t, (x-15)/t, (x-35)/t respectively

Second statement:

Olga distance = x

Wiktor distance = x-22

Their Time is constant:

If it takes (x-15) in t secs,

for x meters will take = xt/(x-15)

Olga and wiktor respectively: xt/(x-15), xt/(x-15) respectively

Their speed:

Speed = distance/time

Olga = (x-15)/t,

Wiktor = (x-22)(x-15)/(xt)

Since speed is constant

Speed for Wiktor in both cases:

(x-35)/t =(x-22)(x-15)/(xt)

x(x-35) =(x-22)(x-15)

x² -35x = x² - 15x -22x +330

-35x = -37x +330

2x = 330

x = 165m

Race held at 165m distance.