Let's break down and solve each problem step-by-step from the image you've uploaded:

1. The ratio of big dogs to small dogs 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?

Explanation:

• The ratio means that for every 2 big dogs, there are 3 small dogs.
• Without knowing the total number of dogs, we can't give an exact number of big and small dogs, but we can infer that the number of big dogs is proportional to $\frac{2}{5}$ of the total, and the number of small dogs is proportional to $\frac{3}{5}$.

If we knew there were, say, 10 dogs total:

• Big dogs: $\frac{2}{5} \times 10 = 4$ big dogs.
• Small dogs: $\frac{3}{5} \times 10 = 6$ small dogs.

Thus, the actual number of dogs must maintain the 2:3 ratio.

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.

Explanation:

• The population of Canada is about 38 million, and the U.S. has around 330 million people.
• To find $x$, we solve the ratio $\frac{5}{x} = \frac{38}{330}$.

$x = \frac{5 \times 330}{38} \approx 43.42$

So, a reasonable value for $x$ would be about 43.

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

Explanation:

• First, convert 35 minutes to hours: $35 \, \text{minutes} = \frac{35}{60} = 0.5833 \, \text{hours}$.
• Use the formula for distance: $\text{distance} = \text{speed} \times \text{time}$.

$\text{distance} = 90 \, \text{km/h} \times 0.5833 \, \text{hours} \approx 52.5 \, \text{km}.$

So, you'll travel about 52.5 km.

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

Explanation:

• 1 kg = 1000 g, so the price per gram is $\frac{3000}{1000} = 3 \, \text{dollars per gram}$.
• For 4 g of saffron, the cost is:

$4 \, \text{g} \times 3 \, \text{\$/g} = 12 \, \text{dollars}.$

A 4 g package would cost $12.

5. 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?

Explanation:

• Convert 32 km/h to metres per second:
  • $1 \, \text{km} = 1000 \, \text{m}$,
  • $1 \, \text{hour} = 3600 \, \text{seconds}$.

So,

$32 \, \text{km/h} = \frac{32 \times 1000}{3600} \approx 8.89 \, \text{m/s}.$

Thus, the water moves at approximately 8.89 metres per second.

Let me know if you'd like further details on any of these solutions!

Relative Questions:

1. If Andrea's class had 15 dogs total, how many big and small dogs are there?
2. How does the population ratio change if Canada’s population grows faster than the U.S.?
3. What if you drove at 100 km/h for 45 minutes, how far would you go?
4. If the price of saffron increases to $3500 per kg, how much would a 4 g package cost?
5. How does the water flow speed at Niagara Falls compare to the average walking speed?

Tip:

Always double-check units in ratio and rate problems to ensure conversions are correctly handled!