Question

25 total animals
to determine a ratio equivalent to the known ratio in this problem, scale down by 4.
amia had
animals drool on her.
set up a proportion and use n for the unknown. then solve using means and extremes.
\\(\frac{\square}{100} = \frac{\square}{\square}\\) animals that drooled
total animals
\\(\square = 100(\square)\\)
\\(\square = n\\)

Explanation:

Step1: Set up the proportion

Let's assume the original ratio of animals that drooled to total animals is \(n:25\). We want to scale it up to a denominator of 100. So the proportion is \(\frac{n}{25}=\frac{x}{100}\), where \(x\) is the number of animals that drooled when the total is 100. Using the means - extremes (cross - multiplication) property: \(25x = 100n\). If we scale down by 4 (assuming the original ratio was \(\frac{n}{25}\) and we want an equivalent ratio), let's assume the original ratio of drooling animals to total animals. If we consider the cross - multiplication for \(\frac{n}{25}=\frac{x}{100}\), by cross - multiplying we get \(25x=100n\). If we assume \(n\) is the number of drooling animals when total is 25. Let's say the ratio of drooling animals to total animals is \(\frac{n}{25}\). When we scale up (since \(100\div25 = 4\)), we have \(\frac{n\times4}{25\times4}=\frac{x}{100}\).

If we use the proportion \(\frac{n}{25}=\frac{x}{100}\), by cross - multiplying (means - extremes: \(a/b = c/d\) implies \(ad = bc\)), we have \(100n=25x\). Solving for \(x\) (if we know \(n\)). But if we assume the ratio is being scaled. Let's assume the number of drooling animals when total is 25 is \(n\). To get the ratio with total 100, we multiply numerator and denominator by 4.

Let's fill the proportion: \(\frac{n}{25}=\frac{x}{100}\). By cross - multiplying \(100n = 25x\). If we assume \(n\) is the number of drooling animals for 25 total animals.

Let's say we use the proportion \(\frac{n}{25}=\frac{x}{100}\). Then \(x=\frac{100n}{25}=4n\). But if we consider the problem statement "scale down by 4" (maybe a mis - statement, likely scale up).

Let's assume the number of drooling animals when total is 25 is \(n\). The proportion is \(\frac{n}{25}=\frac{x}{100}\). Cross - multiplying gives \(25x = 100n\), or \(x = 4n\).

If we assume \(n\) is the number of drooling animals (for 25 total) and we want to find \(x\) (for 100 total).

Let's fill the proportion:

• First blank (numerator of left - hand side): Assume \(n\) (number of drooling animals for 25 total).
• Second blank (numerator of right - hand side): \(n\) (number of drooling animals)
• Third blank (denominator of right - hand side): \(25\) (total animals)
• Fourth blank (left - hand side after cross - multiply): \(100n\)
• Fifth blank (right - hand side after cross - multiply): \(25x\) (but if we solve for \(x\) (number of drooling animals for 100 total), \(x = 4n\). But if we assume the problem is about equivalent ratios.

Let's assume the proportion is \(\frac{n}{25}=\frac{x}{100}\).

Step2: Solve the proportion

Cross - multiply: \(100n=25x\). If we assume \(n\) is the number of drooling animals when total is 25. Let's say \(n = 5\) (for example, if ratio is \(5:25=\frac{1}{5}\), then for 100 total, \(x = 20\) and \(100\times5=25\times20\)).

The proportion \(\frac{n}{25}=\frac{x}{100}\), cross - multiplying gives \(100n = 25x\).

If we fill the proportion:

• \(\frac{n}{25}=\frac{x}{100}\) (where \(n\) is drooling animals for 25 total, \(x\) is drooling animals for 100 total)
• Cross - multiplying: \(100n=25x\)

Answer:

• Proportion: \(\frac{n}{25}=\frac{n}{25}\) (first blank \(n\), second blank \(n\), third blank \(25\))
• Cross - multiply: \(100n = 25x\) (fourth blank \(100n\), fifth blank \(25x\))

If we assume the problem is about equivalent ratios (scaling up from 25 to 100 (a factor of 4)). If the number of drooling animals when total is 25 is \(n\), then when total is 100, it is \(4n\). But since the problem says "scale down by 4" (maybe an error, likely scale up). If we assume \(n\) is the number of drooling animals for 25 total, then for 100 total, using proportion \(\frac{n}{25}=\frac{x}{100}\), \(x = 4n\).

If we consider the blanks:

• \(\frac{n}{25}=\frac{n}{25}\) (proportion: \(\frac{\text{animals that drooled}}{\text{total animals}}\))
• Cross - multiply: \(100\times n=25\times x\)