Question

Find the ratio a : b, given each equality.
a +b=4a

Answer 1

To find the ratio \( a:b \) given the equation \( a + b = 4a \), we can first solve for \( b \) in terms of \( a \).

Starting with the equation:

\[
a + b = 4a
\]

We can isolate \( b \) by subtracting \( a \) from both sides:

\[
b = 4a - a
\]
\[
b = 3a
\]

Now, the ratio \( a:b \) can be expressed as:

\[
\frac{a}{b} = \frac{a}{3a}
\]

We can simplify this ratio:

\[
\frac{a}{b} = \frac{1}{3}
\]

Thus, the ratio \( a:b = 1:3 \).

In conclusion, the final answer is:

\[
\text{The ratio } a : b = 1 : 3
\]