Oscar and Maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles. One entry in the table paired 152 km with 95 miles. If π represents the number of kilometers and π represents the number of miles, who wrote the correct equation that would relate kilometers to miles? Explain why.
95 miles =152 km
1 mile = 152/95 or 1.6 km
this is the acceptable relationship
Since there is none other given, we can't decide who was right
Jason and Whitney each wrote an equation that they felt represented the proportional relationship between the distance in kilometers and distance in miles. One entry in the table paired 182 km with 65 miles.
Jason wrote the equation k = 2.8m. He said the unit rate
represents kilometers per mile.
Whitney wrote the equation k = 0.357m. She said the unit rate 0.357 represents kilometers per mile.
If k represents the number of kilometers and m represents the number of miles, who wrote the correct equation that would relate kilometers to miles? Explain why.
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To determine who wrote the correct equation, we need to analyze the given information and compare it with the equations provided by Oscar and Maria.
Let's start by looking at the given table entry, which pairs 152 km with 95 miles. This means that when there are 152 kilometers, there are 95 miles. We need to find an equation that can represent this connection.
Let's consider Oscar's equation first. If π represents the number of kilometers and π represents the number of miles, Oscar's equation might be π = 2π. This equation states that the number of miles is twice the number of kilometers. However, this does not align with the given data, as 152 km does not correspond to 190 miles.
Now, let's examine Maria's equation. If π represents the number of kilometers and π represents the number of miles, Maria's equation might be π = 0.625π. This equation states that the number of miles is 0.625 times the number of kilometers.
If we substitute 152 for π in Maria's equation, we can calculate the corresponding value of π:
π = 0.625 Γ 152
π = 95
As we can see, Maria's equation does indeed correctly relate kilometers to miles. When π = 152, π = 95, which matches the given table entry.
Therefore, Maria wrote the correct equation that represents the proportional relationship between distance in kilometers and distance in miles. Her equation π = 0.625π is consistent with the given data and accurately describes the relationship between the two variables.