SOLUTION: Jerome wanted to decorate a room by hanging rows of wooden beads across the windows. He strung 1/3 of the beads in 7 long pieces of string and 4/9 of the beads in 16 short piece

Question 1184165: Jerome wanted to decorate a room by hanging rows of wooden beads across the
windows. He strung 1/3 of the beads in 7 long pieces of string and 4/9 of the beads in
16 short pieces of string. He kept the rest of the beads in a container. Each long piece
of string had 15 more beads than each short piece of string.
(a) What fraction of the beads was kept in the container?
(b) How many beads did Jerome use to create his decoration?
Found 2 solutions by Octo-pie7, greenestamps:
Answer by Octo-pie7(11) (Show Source): You can put this solution on YOUR website!
(a) fraction of beads which was kept in container =
1 - (1/3 + 4/9) = 1 - ((3 + 4)/9)
= 1 - 7/9
= (9 - 7)/9
= 2/9
fraction of beads kept in container = 2/9
(b) Let the total beads be x and y be the number of beads in short string
it is given that 1/3 of the beads are used in 7 long pieces of string and each long piece string had 15 more beads than each short string.
-> 1/(x) = 7(y + 15)
-> x = 21(y+15) - (1)
It is given that 4/9 of the beads are used in 16 short pieces of string.
-> 4/9x = 16y
-> x = 16 * 9/4y
-> x = 36y -(1)
from (1) and (2)
36y = 21(y + 15)
-> 36y = 21y + 315
-> 36 - 21y = 315
-> 15y = 315
-> y = 315/15 = 21
using this in (2) we have
x + 36 * 21 = 756
Total number of beads were 756
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

(a) The fraction left in the container is

(b)
1/3 of the beads were used in 7 long strings, so each long string had (1/3)/7 = 1/21 of the total number of beads.
4/9 of the beads were used in 16 short strings, so each short string had (4/9)/16 = 1/36 of the beads.
The number of beads in each long string was 15 more than the number in each short string:

(multiply by the LCM of 36 and 21, which is 21*12=252)

ANSWER: The total number of beads was 756

CHECK:
1/3 of 756 is 252; 7 strings of 252/7=36 beads each
4/9 of 756 is 336; 16 strings of 336/16=21 beads each
36-21=15

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