SOLUTION: At a concert, the ratio of adults to children is 3:8. The ratio of girls to boys is 3:4. What's the ratio of adults to girls? ;

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: At a concert, the ratio of adults to children is 3:8. The ratio of girls to boys is 3:4. What's the ratio of adults to girls? ;       Log On


   

Question 745071: At a concert, the ratio of adults to children is 3:8.
The ratio of girls to boys is 3:4.
What's the ratio of adults to girls?
;
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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At a concert, the ratio of adults to children is 3:8.
a%2Fc = 3%2F8
:
The ratio of girls to boys is 3:4.
g%2Fb = 3%2F4
we know
c = g + b
:
Choose a total, the Least common multiple of (3+8),11; and (3+4),7
LCM = 77
then
a + c = 77
a%2Fc = 3%2F8 therefore dividing 77 by 11 is 7, so we have:
3*7 = 21 adults
and
8*7 = 56 children
then we know
g + b = 56
g%2Fb = 3%2F4 therefore dividing 56 by 7 is 8, so we have
3*8 = 24 girls
4*8 = 32 boys
:
therefore adults to girls:
a%2Fg = 21%2F24 reduces to 7%2F8 is the ratio of adults to girls
:
:
Check out by adding; adults, boys, and girls. 21 + 24 + 32 = 77 total