Question 1208202: Hi
There were 1081 visitors at a museum. 3/7 of the female visitors and 1/4 of the male visitors were children. If the number of female adults was 1/3 of the number of male adults, how many adult visitors were at the museum.
Found 3 solutions by ikleyn, greenestamps, MathTherapy:
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
There were 1081 visitors at a museum.
3/7 of the female visitors and 1/4 of the male visitors were children.
If the number of female adults was 1/3 of the number of male adults,
how many adult visitors were at the museum.
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Let 7x be the number of female visitors and 4y be the number of male visitors.
Then 3x is the number of girls and 4x is the number of adult females;
y is the number of boys and 3y is the number of adult males.
Equations:
7x + 4y = 1081, (1)
 = 4x, (2)
Equation (2) is the same as
y = 4x. (2')
Substitute (2') into (1)
7x + 4*(4x) = 1081
7x + 16x = 1081
23x = 1081
x = 1081/23 = 47.
Hence, y = 4*47 = 188.
ANSWER. The number of adult visitors was 4x + 3y = 4*47 + 3*188 = 752.
Solved.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
3/7 of the female visitors were children:
(Among female visitors, the ratio of children to adults was 3:4)
3x = # of female children
4x = # of female adults
1/4 of the male visitors were children:
(Among male visitors, the ratio of children to adults was 1:3)
y = # of male children
3y = # of male adults
The number of female adults was 1/3 of the number of male adults:
4x = (1/3)(3y) = y
y = 4x
The total number of visitors was 1081:
7x+4y = 1081
7x+4(4x) = 1081
23x = 1081
x = 1081/23 = 47
how many adult visitors were at the museum?
4x+3y = 4x+3(4x) = 16x = 16(47) = 752
ANSWER: 752
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Hi
There were 1081 visitors at a museum. 3/7 of the female visitors and 1/4 of the male visitors were children. If the number of female adults was 1/3 of the number of male adults, how many adult visitors were at the museum.
Let number of males and females, be M, and F, respectively
Since  of females were children, then  of females were adults
Since  of M (males), or  were children, then  of males were adults
Since number of female adults ( ) was  the number of male adults ( ), we
get: 
4(4F) = 7M ----- Cross-multiplying
16F = 7M ----- eq (i)
There were 1,081 vistors, so we get:
M + F = 1,081
F = 1,081 - M ---- eq (ii)
16(1,081 - M) = 7M --- Substituting 1,081 - M for F in eq (i)
16(1,081) - 16M = 7M
16(1,081) = 7M + 16M
16(1,081) = 23M
Number of males, or 
As seen above, number of female adults = 
Also, number of male aduls =
So, number of adults = female adults + male adults = 
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