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 a ratio of $1 : 2$ 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. **Set variables:**
Let $x$ be the amount of wheat flour in cups.
Then bread flour is $2x$ cups because the 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 $x$:**
$$x = \frac{9}{2} \div 3 = \frac{9}{2} \times \frac{1}{3} = \frac{9 \times 1}{2 \times 3} = \frac{9}{6}$$
7. **Simplify the fraction:**
$$\frac{9}{6} = \frac{\cancel{3} \times 3}{\cancel{3} \times 2} = \frac{3}{2} = 1 \frac{1}{2}$$ cups of wheat flour.
8. **Calculate bread flour:**
$$2x = 2 \times \frac{3}{2} = 3$$ cups of bread flour.
**Final answer:**
- Jordan needs $1 \frac{1}{2}$ cups of wheat flour.
- Jordan needs $3$ cups of bread flour.