Answer:
k= 5 over 3 =1.667
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(3)/(2)-((9)/(10)*k)=0
simplify 9/10
3 9
— - (—— • k) = 0
2 10
simplify 3/2
3 9k
— - —— = 0
2 10
Find the Least Common Multiple
The left denominator is : 2
The right denominator is : 10
Least Common Multiple:
10
Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5
Right_M = L.C.M / R_Deno = 1
Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 3 • 5
—————————————————— = —————
L.C.M 10
R. Mult. • R. Num. 9k
—————————————————— = ——
L.C.M 10
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3 • 5 - (9k) 15 - 9k
———————————— = ———————
10 10
Pull out like factors :
15 - 9k = -3 • (3k - 5)
-3 • (3k - 5)
————————————— = 0
10
When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
-3•(3k-5)
————————— • 10 = 0 • 10
10
Now, on the left hand side, the 10 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-3 • (3k-5) = 0
Solve : -3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solve : 3k-5 = 0
Add 5 to both sides of the equation :
3k = 5
Divide both sides of the equation by 3:
k = 5/3 = 1.667
one solution was found
k = 5/3 = 1.667
hope it helps sry its so long
is the sample proportion.