Question

please answer

13 a and b part​

Answer 1

Step-by-step explanation:

Q13

a) let the fraction be x/y

now according to the question

x+y=18 - (i)

and

x/y+2 = 1/3 - (ii)

solving eq (ii)

x/y+2 = 1/3

3x= y+2

3x-y=2 - (iii)

now solving eq (i) & (ii) by elimination method

adding eq i and iii

3x+x-y+y = 18+2

4x=20

x=5

putting value of x in eq i

x+y=18

y=18-5

y=13

fraction = 5/13

b) let the fraction be x/y

now according to the question

x+y=7 - (i)

& 4x = 5y-8 -(ii)

solving eq(ii)

4x=5y-8

5y-4x=8 (iii)

solving eq i and ii by elimination method

multiplying eq (i) by 4 and adding to eq (iii)

4x+4y+5y-4x = 28+8

9y = 36

y = 4

putting value of y in eq(i)

x+y=7

x=7-4

x=3

fraction= 3/4

I m not sure about the answer so u can recheck it.

Answer 2

a.

Let the numerator be x.

Let the denominator be y.

The fraction becomes x/y

The sum of numerator and denominator is 18.

x + y = 18.

Let the above equation be equation 1.

If the denominator is increased by 2, the fraction reduces to 1/3.

$\dfrac{x}{y + 2} = \frac{1}{3} \\ \\ x = \dfrac{y + 2}{3} \\ \\ 3x = y + 2 \\ \\ 3x - y = 2$

Let the above equation be equation 2.

Adding equations 1 and 2.

$(x + y ) + (3x - y)= 18 + 2 \\ \\ x + y + 3x - y = 20 \\ \\ 4x = 20 \\ \\ x = \frac{20}{4} \\ \\ x = 5$

The numerator is 5.

Substitute x = 5 in equation 1.

$x + y = 18 \\ \\ 5 + y = 18 \\ \\ y = 18 - 5 \\ \\ y = 13$

The denominator is 13.

The fraction is 5/13

b.

Let the numerator be x.

Let the denominator be y.

The fraction becomes x/y

The sum of numerator and denominator is 7.

x + y = 7.

Multiplying 4 on both sides.

4 ( x + y ) = 7 × 4

4x + 4y = 28

Let the above equation be equation 1.

Four times the numerator is 8 less than five times the denominator.

4x = 5y -8

5y - 4x = 8

Let the above equation be equation 2.

Adding equations 1 and 2

$(4x + 4y ) +( 5y - 4x)= 28 + 8 \\ \\ 4x + 4y + 5y - 4x = 36 \\ \\ 9y = 36 \\ \\ y = \frac{36}{9} \\ \\ y = 4$

The denominator is 4.

Substitute y = 4 in equation 2.

$5y - 4x = 8 \\ \\( 5 \times 4) - 4x = 8 \\ \\ 20 - 4x = 8 \\ \\ 20 - 8 = 4x \\ \\ 4x = 12 \\ \\ x = \frac{12}{4} \\ \\ x = 3$

The numerator is 3.

The fraction is 3/4.