Una empresa sustituye sus computadores por otros mas modernos. los computadores nuevos son dos tercios del total y hay 33 mas de ellos que computadores antiguos. ¿ cuantos computadores tiene la empresa? ¿cuantos computadores son nuevos?

The question in English
A company replaces its computers with more modern ones. New computers are two thirds of the total and there are 33 more of them than old computers. How many computers does the company have? How many computers are new?

Let
x> numbers of new computers
y> numbers of old computers

we know that
x=y+33> equation 1
x=(2/3)*(x+y)> x-(2/3)x=(2/3)y> (1/3)x=(2/3)y
x=2y> equation 2
1=2
y+33=2y> 2y-y=33> y=33
x=2y> x=2*33> x=66
x+y> 66+33> 99 totally computers

the answers are
Part A) the company have 99 computers
part B) The numbers of new computers are 66

the answer in spanish

Hacemos
x> numero de computadoras nuevas
y> numero de computadoras viejas

sabemos que
x=y+33> ecuacion 1
x=(2/3)*(x+y)> x-(2/3)x=(2/3)y> (1/3)x=(2/3)y
x=2y> ecuacion 2
1=2
y+33=2y> 2y-y=33> y=33
x=2y> x=2*33> x=66
x+y> 66+33> 99 computadoras en total

Las respuestas son
Parte A) la empresa tiene un total de 99 computadoras
Parte B) El numero de computadoras nuevas es 66

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.