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Let's work through these questions one by one.

### 1. The ratio of big dogs to small ones in Andrea’s dog obedience class is 2:3. How many big dogs and small dogs do you think are probably in her class? Why?

A ratio of 2:3 means that for every 2 big dogs, there are 3 small dogs. To find the total number of dogs, we need to assume that this ratio applies across the whole class. 

Let's say there are 5 parts total in this ratio (2 parts big dogs and 3 parts small dogs).

If we were to estimate the total number of dogs in the class (say, 10 dogs), we could divide them into parts like this:
- 2 parts out of 5 are big dogs
- 3 parts out of 5 are small dogs.

This would give us 4 big dogs (since 2/5 of 10 is 4) and 6 small dogs (since 3/5 of 10 is 6).

### 2. The ratio of the population of Canada to the population of the United States is 5:x. What might be a reasonable value for x? Explain.

The population of Canada is about 40 million, and the population of the United States is about 335 million. To estimate the ratio, divide these two numbers:

\[
\text{Ratio} = \frac{40}{335} \approx 0.12
\]

So, the ratio 5:x means that for every 5 people in Canada, there are **x** people in the United States. We can find **x** by setting up the proportion:

\[
\frac{5}{x} = 0.12
\]

Solving for **x**:

\[
x = \frac{5}{0.12} \approx 41.67
\]

A reasonable value for **x** is around **42**.

### 3. If you drive at 90 km/h for 35 minutes, about how far will you get?

First, convert the time from minutes to hours:

\[
35 \, \text{minutes} = \frac{35}{60} = 0.583 \, \text{hours}
\]

Now, use the formula for distance:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

\[
\text{Distance} = 90 \, \text{km/h} \times 0.583 \, \text{hours} \approx 52.47 \, \text{km}
\]

You would drive about **52.5 kilometers**.

### 4. Saffron costs $3000 for 1 kg. About how much would a package of 4 g of saffron cost?

First, convert 4 grams to kilograms:

\[
4 \, \text{g} = 0.004 \, \text{kg}
\]

Now, multiply the price per kilogram by the weight in kilograms:

\[
\text{Cost} = 3000 \times 0.004 = 12
\]

A package of 4 g of saffron would cost about **$12**.

### 5. The Niagara River flows at about 32 km/h at the crest of Niagara Falls. How fast does the water move in meters per second?

Convert kilometers per hour to meters per second. We know:

\[
1 \, \text{km} = 1000 \, \text{m}
\]
\[
1 \, \text{hour} = 3600 \, \text{seconds}
\]

So:

\[
\text{Speed in m/s} = \frac{32 \, \text{km/h} \times 1000 \, \text{m/km}}{3600 \, \text{s/h}} = \frac{32000}{3600} \approx 8.89 \, \text{m/s}
\]

The water moves at about **8.9 meters per second**.

---

Would you like more details on any of these solutions? 

Here are 5 follow-up questions to expand on this information:
1. How could we adjust the ratio of big to small dogs if there were 15 total dogs?
2. If the population ratio between Canada and the U.S. changed, how would that affect **x**?
3. What if the speed was reduced to 70 km/h in question 3? How far would you travel in 35 minutes?
4. How much would 10 g of saffron cost at the same price rate?
5. How would the flow of water change if the speed at Niagara Falls was doubled?

**Tip:** Always convert units properly, especially when working between different systems (e.g., kilometers to meters or hours to seconds).

The ratio of big dogs to small ones in Andrea’s dog obedience class is 2:3. How many big dogs and small dogs do you think are probably in her class? Why?
The ratio of the population of Canada to the population of the United States is 5:x. What might be a reasonable value for x? Explain.
If you drive at 90 km/h for 35 minutes, about how far will you get?
Saffron costs $3000 for 1 kg. About how much would a package of 4 g of saffron cost?
The Niagara River flows at about 32 km/h at the crest of Niagara Falls. How fast does the water move in metres per second?

Learn how to solve problems involving the ratio of big to small dogs, population comparisons, calculating driving distances, estimating saffron costs, and converting flow rate at Niagara Falls from km/h to meters per second. Suitable for Grade 7 students.

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