Respuesta :
Answer:
1) [tex]\frac{x+3}{2x-5}=\frac{3}{2}[/tex] (x ≠ 2,5)
=> 2(x + 3) = 3(2x - 5)
⇔ 2x + 6 = 6x - 15
⇔ 4x = 6 + 15
⇔ 4x = 21
⇔ x = 5,25
2) [tex]\frac{5y-2}{2y+8}=\frac{5}{6}[/tex] (y ≠ -4)
⇒6( 5y - 2) = 5(2y + 8)
⇔30y - 12 = 10y + 40
⇔ 20y = 52
⇔ y = 2,6
3) the denominator of the rational number is x (x ≠ 0)
because the denominator is greater than the numerator by 6
=> the numerator is x - 6
If the numerator is decreased by 1 and the denominator increased
by 1 , the number obtained is 1/3. so we have:
[tex]\frac{x-7}{x+1}=\frac{1}{3}[/tex]
⇒ 3(x - 7) = x + 1
⇔ 3x - 21 = x + 1
⇔ 2x = 22
⇔ x = 11
with x = 11 => the rational number is 5/11
4) the number we need to find is ab (a ≠ 0)
because Sum of the digits of this number is 8
=> a + b = 8 (*)
When we interchange the digits , it is found that the resulting new number is less than the original number by 18, we have:
ab - ba = 18
⇔ 10a + b - (10b + a) = 18
⇔ 9( a - b) = 18
⇔ a - b = 2 (**)
(*)(**) => a + b = 8
a - b = 2
=> a = 5
b = 3
=> the original number is 53
5) the present Arjun's age is x (years old)( x, y E N*)
the present Shriya's age is y
because now, Arjun is twice as old as Shriya => x = 2y
Five years ago, his age was three times Shriya’s age, we have:
=> x - 5 = 3(y - 5)
⇔ x - 5 = 3y - 15
⇔ 3y - x = 10
but x = 2y => y = 10
=> x = 20
so now, Arjun is 20 years old, Shriya is 10 years old
Step-by-step explanation:
