Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "0.05" was replaced by "(05/100)". 2 more similar replacement(s)
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(12/100)*x+(5/100)*(6000-x)-(580)=0
Step by step solution :
Step 1 :
1
Simplify ——
20
Equation at the end of step 1 :
12 1
((——— • x) + (—— • (6000 - x))) - 580 = 0
100 20
Step 2 :
Equation at the end of step 2 :
12 (6000 - x)
((——— • x) + ——————————) - 580 = 0
100 20
Step 3 :
3
Simplify ——
25
Equation at the end of step 3 :
3 (6000 - x)
((—— • x) + ——————————) - 580 = 0
25 20
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 25
The right denominator is : 20
| Prime Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
|---|---|---|---|
| 5 | 2 | 1 | 2 |
| 2 | 0 | 2 | 2 |
| Product of all Prime Factors | 25 | 20 | 100 |
Least Common Multiple:
100
Calculating Multipliers :
4.2 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 = 4
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
4.3 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. 3x • 4 —————————————————— = —————— L.C.M 100 R. Mult. • R. Num. (6000-x) • 5 —————————————————— = ———————————— L.C.M 100
Adding fractions that have a common denominator :
4.4 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:
3x • 4 + (6000-x) • 5 7x + 30000
————————————————————— = ——————————
100 100
Equation at the end of step 4 :
(7x + 30000)
———————————— - 580 = 0
100
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 100 as the denominator :
580 580 • 100
580 = ——— = —————————
1 100
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
(7x+30000) - (580 • 100) 7x - 28000
———————————————————————— = ——————————
100 100
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
7x - 28000 = 7 • (x - 4000)
Equation at the end of step 6 :
7 • (x - 4000)
—————————————— = 0
100
Step 7 :
When a fraction equals zero :
7.1 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:
7•(x-4000)
—————————— • 100 = 0 • 100
100
Now, on the left hand side, the 100 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
7 • (x-4000) = 0
Equations which are never true :
7.2 Solve : 7 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
7.3 Solve : x-4000 = 0
Add 4000 to both sides of the equation :
x = 4000
One solution was found :
x = 4000How did we do?
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