How many beads does Belinda use to make a bracelet?

Question

she uses 1/3 beads for bracelet and 3/5 beads for necklace. She uses 36 more beads on necklace. How many beads does Belinda use to make the bracelet?

Answer 1

Here's what we know: b = bracelet n = necklace, l = left over beads

b + n + l = x, where x is total number of beads

n = b + 36

 

if x = 1, then

f(1) = 1/3 + 3/5 + l

f(1) = 5/15 + 9/15 + l

f(1) = 5/15 + 9/15 + 1/15

 

For every 5 on the bracelet, there' s 9 for the necklace (with one extra).

9 - 5 = 4

36 / 4 = 9

 

In other words, when keeping it proportional, to reach 36 more beads on the necklace, there have been nine iterations of 5 for bracelet:9 for necklace

 

5 beads * 9 iterations = 45 beads for the bracelet.

9 beads * 9 iterations = 81 beads for necklace.

 

Now to check our answer:

81 - 45 = 36, which is how many the problem told us how many beads the necklace has over the bracelet

 

Answer 2

x=# of beads

(1/3)x+36=(3/5)x

36=(3/5)x-(1/3)x

36=(9/15)x-(5/15)x

36=(4/15)x

multiply both sides by (15/4)

(15/4)(36)=(15/4)(4/15)x

15*9=x

135=x

x=135 beads in all

(1/3)*(135)=45 beads to make the bracelet