Question 1184165
<br>
(a) The fraction left in the container is<br>
{{{1-(1/3)-(4/9)=1-3/9-4/9=1-7/9=2/9}}}<br>
(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:<br>
{{{(1/21)x=(1/36)x+15}}}
{{{(1/21)x-(1/36)x=15}}}
(multiply by the LCM of 36 and 21, which is 21*12=252)
{{{12x-7x=15*252}}}
{{{5x=15*252}}}
{{{x=3*252=756}}}<br>
ANSWER: The total number of beads was 756<br>
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<br>