The ratio of the numerator to the denominator of a certain fraction is three to five. if two is added to the numerator and
five is subtracted from the denominator, the new fraction reduces to four fifths. find the onginal fraction

The original fraction is  

Step-by-step explanation:

Given as :

The ratio of numerator to denominator = 3 : 5

Let The numerator = 3 x

Let The denominator = 5 x

Again

If two is added to the numerator and  five is subtracted from the denominator, the new fraction reduces to four fifths.

So, =

Or, 5 × (3 x + 2) = 4 × (5 x - 5)

Or, 15 x + 10 = 20 x - 20

Or, 20 x - 15 x = 10 + 20

or, 5 x = 30

∴  x =

i.e x = 6

So, The numerator = 3 × 6 = 18

And The denominator = 5 × 6 = 30

∴ Original fraction =

Or, Original fraction = =

Hence, The original fraction is    Answer

x

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!