Question

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?
red beads

Answer 1

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

\[
\boxed{15}
\]