Question

1. The sum of three consecutive even numbers is 72. Find the numbers.
17
2. Half more than a rational number multiplied by 7 gives Find the rational numbe
2
The numerator of a fraction is 3 more than the denominator If the numerator and​

Answer 1

Answers:

1) Let the three consecutive even numbers be x, x+2 and x+4.

Given,

[tex]\sf{x+x+2+x+4=74} [/tex]

[tex]\sf{3x+6=72} [/tex]

[tex]\begin{gathered}\sf{3x=72-6}\\\end{gathered} [/tex]

[tex]\sf{3x=66} [/tex]

[tex]\sf{x=66/3} [/tex]

$\sf{x=22}$

Therefore the consecutive even numbers are:

x = 22, x + 2 = 24, x + 4 = 26

= 22, 24, 26

2) Correct Question:

Half more than a rational number multiplied by 7 gives 17/2. Find the rational number.

Let the unknown number be x.

Given,

[tex]\sf{(x+\dfrac{1}{2})\times7=\dfrac{17}{2}} [/tex]

[tex]\sf{x+\dfrac{1}{2}=\dfrac{17}{2}\times\dfrac{1}{7}} [/tex]

[tex]\sf{x+\dfrac{1}{2}=\dfrac{17}{4}} [/tex]

[tex]\sf{x=\dfrac{17}{14}-\dfrac{1}{2}} [/tex]

[tex]\sf{x=\dfrac{10}{14}} [/tex]

[tex]\sf{x=\dfrac{5}{7}} [/tex]

3) Correct Question:

The numerator of a fraction is 3 more than the denominator If the numerator and​ the denominator are increased by 5 the fraction becomes 10/7. Find the fraction.

Let the denominator be x.

So, numerator = x + 3

Given,

[tex]\sf{\dfrac{x+3+5}{x+5}=\dfrac{10}{7}} [/tex]

[tex]\sf{\dfrac{x+8}{x+5}=\dfrac{10}{7}} [/tex]

Through cross multiplication:

[tex]\sf{7(x+8)=10(x+5)} [/tex]

[tex]\sf{7x+56=10x+50} [/tex]

Moving the constants and variables to same side:

[tex]\sf{56-50=10x-7x} [/tex]

[tex]\sf{3x=6} [/tex]

[tex]\sf{x=\dfrac{6}{3}} [/tex]

[tex]\sf{x=2} [/tex]

x = 2

x + 3 = 2 + 3 = 5

So the fraction is 5/2.