Question: Jordan invents a bread recipe using both whole wheat flour and bread flour. The ratio of wheat flour to bread flour is $1 : 2$. The recipe requires a total of $4 \frac{1}{2}$ cups of flour to make one loaf. How many cups of each type of flour does Jordan need?
1. **State the problem:** Jordan needs to mix whole wheat flour and bread flour in the ratio $1 : 2$ to get a total of $4 \frac{1}{2}$ cups of flour.
2. **Convert mixed number to improper fraction:**
$$4 \frac{1}{2} = \frac{9}{2}$$ cups total.
3. **Define variables:**
Let $x$ be the cups of whole wheat flour.
Then bread flour is $2x$ cups (because ratio is $1:2$).
4. **Write the equation for total flour:**
$$x + 2x = \frac{9}{2}$$
5. **Simplify the equation:**
$$3x = \frac{9}{2}$$
6. **Solve for $x$:**
$$x = \frac{\frac{9}{2}}{3} = \frac{9}{2} \times \frac{1}{3} = \frac{9}{6} = \frac{3}{2}$$
7. **Interpret the result:**
Whole wheat flour needed is $\frac{3}{2}$ cups or $1.5$ cups.
8. **Calculate bread flour:**
$$2x = 2 \times \frac{3}{2} = 3$$ cups.
**Final answer:**
Jordan needs $1.5$ cups of whole wheat flour and $3$ cups of bread flour.