`(a)/(5)=(b)/(5)=(c )/(3)=(d)/(4)` find `a : b :c :d=?`

Answer

To solve the problem `(a)/(5) = (b)/(5) = (c)/(3) = (d)/(4)` and find the ratio `a : b : c : d`, we can follow these steps:

### Step-by-Step Solution:

1. **Set a common variable**:
Let us denote the common value of the ratios as `k`. Therefore, we can express `a`, `b`, `c`, and `d` in terms of `k`:
\[ \frac{a}{5} = k \implies a = 5k \]
\[ \frac{b}{5} = k \implies b = 5k \]
\[ \frac{c}{3} = k \implies c = 3k \]
\[ \frac{d}{4} = k \implies d = 4k \]

2. **Write the ratio**:
Now we can write the ratio `a : b : c : d` using the expressions we derived:
\[ a : b : c : d = 5k : 5k : 3k : 4k \]

3. **Simplify the ratio**:
Since all terms contain `k`, we can simplify the ratio by dividing each term by `k`:
\[ a : b : c : d = 5 : 5 : 3 : 4 \]

4. **Final ratio**:
Thus, the final ratio of `a : b : c : d` is:
\[ a : b : c : d = 5 : 5 : 3 : 4 \]