Give a is one-fifth of b, find c such tat `a:b = 6:c.`

Answer

To solve the problem step by step, we will follow the given information and apply the concepts of ratios and proportions.

### Step 1: Understand the relationship between a and b
We know from the problem that \( a \) is one-fifth of \( b \). This can be expressed mathematically as:
\[ a = \frac{1}{5}b \]

### Step 2: Express b in terms of a
From the equation \( a = \frac{1}{5}b \), we can rearrange it to express \( b \) in terms of \( a \):
\[ b = 5a \]

### Step 3: Set up the ratio a:b and the given ratio 6:c
We need to find \( c \) such that the ratio \( a:b \) is equal to \( 6:c \). We can write this as:
\[ \frac{a}{b} = \frac{6}{c} \]

### Step 4: Substitute the value of b
Now, we substitute the expression for \( b \) (which is \( 5a \)) into the ratio:
\[ \frac{a}{5a} = \frac{6}{c} \]

### Step 5: Simplify the left side of the equation
The left side simplifies to:
\[ \frac{1}{5} = \frac{6}{c} \]

### Step 6: Cross-multiply to solve for c
Cross-multiplying gives us:
\[ c \cdot 1 = 5 \cdot 6 \]
\[ c = 30 \]

### Final Answer
Thus, the value of \( c \) is:
\[ c = 30 \]

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