Question

in the city of erie, 8 meters of snow fell in 20 days. at this rate, how much snow would fall in 80 days?
(a) let a be the unknown amount of snow that would fall (in meters). using the values below, create a proportion that can be used to find a.
values: a, 8, 20, 80
__ = __
(b) use the proportion from part (a) to find the amount of snow that would fall in 80 days. do not round any computations.
□ meters

Explanation:

Part (a)

Step1: Identify the ratio

The rate of snowfall is constant, so the ratio of snow (in meters) to days should be equal. So we have snow/days for the first case and snow/days for the second case.
The first case: 8 meters in 20 days, so $\frac{8}{20}$. The second case: $A$ meters in 80 days, so $\frac{A}{80}$. So the proportion is $\frac{8}{20}=\frac{A}{80}$ (or $\frac{A}{80}=\frac{8}{20}$, or also $\frac{20}{8}=\frac{80}{A}$ etc., but the most straightforward is snow over days equal for both).

Step2: Fill the proportion

Using the values, we put the snow amounts in the numerators and days in the denominators (or vice versa, but consistent). So $\frac{8}{20}=\frac{A}{80}$ (or other consistent ratios like $\frac{20}{8}=\frac{80}{A}$, but the first is more intuitive as snow per day). So the boxes would be filled with 8, 20, A, 80 (or other order as long as the ratio is consistent). For example, $\frac{8}{20}=\frac{A}{80}$.

Part (b)

Step1: Set up the proportion

From part (a), we have $\frac{8}{20}=\frac{A}{80}$.

Step2: Cross - multiply

Cross - multiplying gives $20\times A = 8\times80$.

Step3: Solve for A

First, calculate $8\times80 = 640$. Then, $A=\frac{640}{20}$.

Step4: Simplify

$\frac{640}{20}=32$.

Answer:

(Part a):
$\frac{8}{20}=\frac{A}{80}$ (or other consistent proportion like $\frac{A}{80}=\frac{8}{20}$, $\frac{20}{8}=\frac{80}{A}$, $\frac{80}{A}=\frac{20}{8}$)