Helen's weight is 3/5 of that her sister. If the difference of their weight is 14kg,find weight of Helen 

Let Helen's weight be \( H \) and her sister's weight be \( S \).

According to the problem, we know two things:

1. Helen's weight is \( \frac{3}{5} \) of her sister's weight:
   \[
   H = \frac{3}{5}S
   \]

2. The difference between their weights is 14 kg:
   \[
   S - H = 14
   \]

### Step 1: Substitute \( H = \frac{3}{5}S \) into the second equation:
\[
S - \frac{3}{5}S = 14
\]

### Step 2: Solve for \( S \):
\[
\frac{5}{5}S - \frac{3}{5}S = 14
\]
\[
\frac{2}{5}S = 14
\]

### Step 3: Multiply both sides by 5 to eliminate the fraction:
\[
2S = 70
\]

### Step 4: Solve for \( S \):
\[
S = 35
\]

So, Helen's sister weighs 35 kg.

### Step 5: Calculate Helen's weight:
\[
H = \frac{3}{5} \times 35 = 21 \, \text{kg}
\]

Thus, Helen's weight is **21 kg**.

Would you like more details or have any questions? Here are some related problems you could try:

1. If Helen’s sister weighed 40 kg, what would Helen’s weight be?
2. What is the ratio of Helen’s weight to their total weight?
3. If Helen gained 5 kg, what would be the new difference in their weights?
4. If the sum of their weights was 100 kg, how much would Helen weigh?
5. If their weight difference was 10 kg, what would Helen’s new weight be?

**Tip**: Always double-check your equations by substituting values back into the original statements.

Helen's weight is 3/5 of that of her sister. If the difference of their weight is 14 kg, find the weight of Helen.

Solve the problem where Helen's weight is 3/5 of her sister's, and their weight difference is 14 kg. Learn the step-by-step algebraic solution, including key concepts of ratios and linear equations. Ideal for students in Grades 6-8.

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