Solving for Total Dogs: Analyzing 1,220,500 Dalmatian Spots Using Fractions

To solve this problem, we need to determine how many Dalmatians participated based on the number of spots each group has and the total spots counted.

Let's denote the total number of dogs as $x$.

According to the data provided:

• One out of every four dogs has 708 spots, which gives us $\frac{1}{4}x \times 708$ spots for this group.
• One out of every three dogs has 660 spots, which gives us $\frac{1}{3}x \times 660$ spots for this group.
• 625 dogs have 1000 spots each, contributing $625 \times 1000$ spots.

We need to sum these contributions to get the total spot count of 1,220,500.

The total equation for spots is:

$\frac{1}{4}x \times 708 + \frac{1}{3}x \times 660 + 625 \times 1000 = 1,220,500$

Let's simplify this equation:

$\frac{1}{4}x \times 708 = 177x$ $\frac{1}{3}x \times 660 = 220x$

Thus, the equation becomes:

$177x + 220x + 625 \times 1000 = 1,220,500$ $397x + 625,000 = 1,220,500$

Subtract 625,000 from both sides:

$397x = 595,500$

Now, divide by 397:

$x = \frac{595,500}{397} = 1500$

The number of dogs that participated in the study is therefore $1500$.