Question

Rita got three colors of beads, half of them are pink. She used all her pink beads to make some bracelets. If the number of pink beads she used for each bracelet is one eighths of the total number of beads, how many bracelets did she make?

Answer 1

Answer: she made 4 bracelets.

Step-by-step explanation:

Let x, y, z are the number of three kinds of beads, where x= number of pink beads.

As per given, number of pink beads= half of total beads  

$\Rightarrow\ x=\dfrac{1}{2}(x+y+z)\\\\\Rightarrow 2x= x+y+z\\\\\Rightarrow\ x= y+z\ \ \ ...(i)$

Also, She used all pink beads,  Number of pink beads she used for each bracelet= one eighths of the total number of beads

$\dfrac{1}{8}(x+y+z)\\\\=\dfrac{1}{8}(x+x)\ \ \ [ {\text{From (i)}}]$

$=\dfrac{1}{8}(2x)\\\\=\dfrac{x}{4}$bracelets =

Number of bracelets = (Number of pink beads) ÷ (Number of pink beads used for each bracelet)

$=\dfrac{x}{\dfrac{x}{4}}=4$

Hence, she made 4 bracelets.