Question
In the map below, the path from the whales to the sharks is parallel to the path from the penguins to the fish tanks.
Set up and solve the proportion to find the distance between the penguins and the fish tank.
(3 points)
Set up the proportion: 54/30=
NOTE: Type the correct fraction into the box to receive credit.
Cross Multiply: 30x=
NOTE: Type the correct numerical answer into the box to receive credit.
Solve for x: x=
feet
NOTE: Type the correct numerical answer into the box to receive credit.
Set up and solve the proportion to find the distance between the penguins and the fish tank.
(3 points)
Set up the proportion: 54/30=
NOTE: Type the correct fraction into the box to receive credit.
Cross Multiply: 30x=
NOTE: Type the correct numerical answer into the box to receive credit.
Solve for x: x=
feet
NOTE: Type the correct numerical answer into the box to receive credit.
Answers
GPT-4o mini
Let's set up the proportion based on the given information:
The proportion can be represented as follows:
\[
\frac{54}{30} = \frac{x}{d}
\]
where \(d\) is the distance between the penguins and the fish tanks, and we need to solve for \(d\).
Cross-multiplying gives us:
\[
54d = 30x
\]
To solve for \(d\):
\[
d = \frac{30x}{54}
\]
Now, let's simplify the fraction:
\[
d = \frac{5x}{9}
\]
Now that we have our expression for \(d\), we can plug in the value of \(x\) to find the distance.
Assuming we've calculated or need to assume some value of \(x\) based on the context:
If \(x\) is given or can be calculated, you would then plug in that value to solve for \(d\). For example, if \(x = 54\):
\[
d = \frac{5(54)}{9} = \frac{270}{9} = 30 \text{ feet}
\]
So, the full solution to your question would require a specific value for \(x\), or it could be a direct statement based on derived ratios from distances given. Fill in the blanks with numbers as appropriate based on actual distances or values provided in a complete context.
The proportion can be represented as follows:
\[
\frac{54}{30} = \frac{x}{d}
\]
where \(d\) is the distance between the penguins and the fish tanks, and we need to solve for \(d\).
Cross-multiplying gives us:
\[
54d = 30x
\]
To solve for \(d\):
\[
d = \frac{30x}{54}
\]
Now, let's simplify the fraction:
\[
d = \frac{5x}{9}
\]
Now that we have our expression for \(d\), we can plug in the value of \(x\) to find the distance.
Assuming we've calculated or need to assume some value of \(x\) based on the context:
If \(x\) is given or can be calculated, you would then plug in that value to solve for \(d\). For example, if \(x = 54\):
\[
d = \frac{5(54)}{9} = \frac{270}{9} = 30 \text{ feet}
\]
So, the full solution to your question would require a specific value for \(x\), or it could be a direct statement based on derived ratios from distances given. Fill in the blanks with numbers as appropriate based on actual distances or values provided in a complete context.