Simultaneous Equation

At a flower show which 1250 attended, outsiders were charged $1, villagers $ 0.5 and school children $ 0.05. The total receipt from the flower show was $695. There were 3 times as many villagers as outsiders. How many outsiders came to the show?




Answer:

Let the number of outsiders be x.
Let the number of school children be y.

Condition 1
x + 3x + y = 1250
or, 4x + y = 1250
or, y = 1250 - 4x   -------------(1)

Condition 2
1.x + 0.5.3.x +0.05y = 695
or x + 1.5x + 0.05y = 695
or, 2.5x + 0.05y = 695
Multiplying throughout by 20, we get
50x + y = 695 x 20   -----------(2)

Substituting (1) in (2),we get

50x + 1250 - 4x = 695 x 20
or, 46x = 12650
or, x =  275

So, the number of outsiders was 275.

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