Question: This table shows a proportional relationship between the number of cups of bananas and strawberries used for a smoothie.
a.) Enter the number of cups of bananas used for 1 cup of strawberries.
b.) Enter the constant of proportionality that relates the quantities $x$ and $y$.
c.) Enter an equation that relates the quantities.
Cups of Bananas
($x$)
Cups
Strawberries
($y$)
1 $\frac{2}{25}$
5 $\frac{2}{5}$
2 $\frac{18}{25}$
13 $\frac{3}{5}$
1. **State the problem:** We have a proportional relationship between cups of bananas ($x$) and cups of strawberries ($y$) with given data points:
- $x=1 \frac{2}{25} = \frac{27}{25}$ cups, $y=5 \frac{2}{5} = \frac{27}{5}$ cups
- $x=2 \frac{18}{25} = \frac{68}{25}$ cups, $y=13 \frac{3}{5} = \frac{68}{5}$ cups
2. **Find the number of cups of bananas used for 1 cup of strawberries:**
Since $y$ is strawberries and $x$ is bananas, for 1 cup of strawberries, find $x$ such that $y=1$.
3. **Find the constant of proportionality $k$:**
The relationship is $y = kx$ or $x = \frac{y}{k}$.
Using the first pair:
$$k = \frac{y}{x} = \frac{\frac{27}{5}}{\frac{27}{25}} = \frac{27}{5} \times \frac{25}{27} = 5$$
4. **Check with the second pair:**
$$k = \frac{\frac{68}{5}}{\frac{68}{25}} = \frac{68}{5} \times \frac{25}{68} = 5$$
5. **Interpretation:** The constant of proportionality $k=5$ means strawberries are 5 times the bananas.
6. **Find cups of bananas for 1 cup of strawberries:**
Since $y = 5x$, then
$$x = \frac{y}{5}$$
For $y=1$ cup strawberries:
$$x = \frac{1}{5}$$
7. **Write the equation relating $x$ and $y$:**
$$y = 5x$$
**Final answers:**
- a) Number of cups of bananas for 1 cup of strawberries is $\frac{1}{5}$.
- b) Constant of proportionality $k = 5$.
- c) Equation relating quantities: $$y = 5x$$