Question: Two numbers total is $112$ and ratio is $5:3$
1. **State the problem:** We are given two numbers whose total sum is $112$ and their ratio is $5:3$. We need to find the two numbers.
2. **Formula and rules:** If two numbers are in the ratio $a:b$, then the numbers can be represented as $5x$ and $3x$ respectively.
3. **Set up the equation:** Since their total is $112$, we write:
$$5x + 3x = 112$$
4. **Simplify the equation:**
$$8x = 112$$
5. **Solve for $x$:**
$$x = \frac{112}{8}$$
6. **Simplify the fraction:**
$$x = \cancel{\frac{112}{8}} = 14$$
7. **Find the two numbers:**
First number: $5x = 5 \times 14 = 70$
Second number: $3x = 3 \times 14 = 42$
8. **Check:**
Sum: $70 + 42 = 112$
Ratio: $\frac{70}{42} = \frac{5}{3}$ which matches the given ratio.
**Final answer:** The two numbers are $70$ and $42$.