Question 1208202
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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 {{{matrix(1,3, (3/7)F, or, 3F/7))}}} of females were children, then {{{matrix(1,3, (1 - 3/7)F, or, 4F/7)}}} of females were adults
Since {{{1/4}}} of M (males), or {{{M/4}}} were children, then {{{matrix(1,3, (1 - 1/4)M, or, 3M/4)}}} of males were adults
Since number of female adults ({{{4F/7}}}) was {{{1/3}}} the number of male adults ({{{3M/4}}}), we
get: {{{matrix(2,3, 4F/7, "=", (1/3)(3M/4), 4F/7, "=", M/4)}}}
   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 {{{matrix(1,9, M, "=", 16("1,081")/23, "=", 16(47cross("1,081"))/cross(23), "=", 16(47), "=", 752)}}}

As seen above, number of female adults = {{{matrix(1,3, 4F/7, "=", M/4)}}}
Also, number of male aduls = {{{3M/4}}}
So, number of adults = female adults + male adults = {{{highlight_green(matrix(1,7, M/4 + 3M/4, "=", 4M/4, "=", M, "=", highlight(752)))}}}</pre>