Question

Sarah is making a bead necklace. For every 2 red beads, she uses 5 blue beads. If she uses 49 beads in total, how many are red?



(1 point)
red beads

Answer 1

Let's denote the number of red beads as \( r \) and the number of blue beads as \( b \).

According to the problem, for every 2 red beads, there are 5 blue beads. This gives us the ratio:

\[
\frac{r}{b} = \frac{2}{5}
\]

We can express \( b \) in terms of \( r \):

\[
b = \frac{5}{2}r
\]

Additionally, we know that the total number of beads used by Sarah is 49:

\[
r + b = 49
\]

Now we can substitute \( b \) into the total bead equation:

\[
r + \frac{5}{2}r = 49
\]

Combining the terms on the left side:

\[
\frac{2}{2}r + \frac{5}{2}r = \frac{7}{2}r
\]

So we have:

\[
\frac{7}{2}r = 49
\]

To solve for \( r \), we first multiply both sides by 2:

\[
7r = 98
\]

Now, divide both sides by 7:

\[
r = 14
\]

Therefore, the number of red beads Sarah used is \( \boxed{14} \).