Pam makes a necklace with three colors of beads. For every 10 blue beads she strings on the necklace, she uses 7 yellow beads and 3 red beads. The necklace has a total of 100 beads. How many red beads does she use?

Let's denote the number of sets of beads Pam uses as \( x \). According to the problem, for each set of beads, she uses:

• 10 blue beads
• 7 yellow beads
• 3 red beads

This means each set contains a total of:

\[ 10 + 7 + 3 = 20 \text{ beads} \]

If she strings \( x \) sets of beads, the total number of beads can be expressed as:

\[ 20x \]

We know that the total number of beads in the necklace is 100, so we can set up the equation:

\[ 20x = 100 \]

To find \( x \), we divide both sides by 20:

\[ x = \frac{100}{20} = 5 \]

Now that we know \( x = 5 \), we can find the number of red beads used. Since she uses 3 red beads per set, the total number of red beads is:

\[ 3x = 3 \times 5 = 15 \]

Therefore, the number of red beads she uses is

\[ \boxed{15} \]