3k/5+44=12k/25+8
Please help me solve this and show your work thanks
multiply by 25 to clear fractions:
75k + 1100 = 12k + 200
63k = -900
k = -100/7
To solve the equation 3k/5 + 44 = 12k/25 + 8, we need to simplify and isolate the variable k.
Let's start by simplifying both sides of the equation step-by-step.
Step 1: Simplify the fractions on both sides:
On the left side, we have 3k/5 which cannot be simplified further.
On the right side, we need to find a common denominator for 12k/25 and 8. Since 25 can be evenly divided by 5, the common denominator is 25. So, we can rewrite the equation as:
3k/5 + 44 = (12k/25) + (8 * 25/25)
= 12k/25 + 200/25
= (12k + 200)/25
Now, the equation becomes:
3k/5 + 44 = (12k + 200)/25
Step 2: Multiply throughout by 25 to eliminate the fraction:
We multiply both sides of the equation by 25 to eliminate the fraction on the right side:
25 * (3k/5 + 44) = 25 * (12k + 200)/25
This simplifies to:
(25 * 3k)/5 + (25 * 44) = 12k + 200
15k + 1100 = 12k + 200
Step 3: Move all terms involving k to one side and the constant terms to the other side:
Subtract 12k from both sides of the equation:
15k + 1100 - 12k = 12k + 200 - 12k
This simplifies to:
3k + 1100 = 200
Step 4: Move the constant term to the other side:
Subtract 1100 from both sides of the equation:
3k + 1100 - 1100 = 200 - 1100
This simplifies to:
3k = -900
Step 5: Solve for k by dividing both sides of the equation by 3:
(3k)/3 = (-900)/3
This simplifies to:
k = -300
Therefore, the value of k that satisfies the equation is k = -300.