Indira is having 34 tulips, 68 daffodils and 102 hyacinths , altogether 204 flowers in her spring garden.
Given, In Indira's springtime garden, there are three times more hyacinths than tulips and half as many daffodils as tulips.
let the number of tulips be = x
the number of daffodils be = y
the number of hyacinths be = z
hence according to the question,
tulips are (x) = 1/2 (y) = y/2
hyacinths are (z) = 3(x) = 3x
therefore, total flowers = 204
tulips ₊ daffodils ₊ hyacinths = 204
y/2 ₊ y ₊ 3x = 204
substitute x value in the above equation.
y/2 ₊ y ₊ 3(y/2) = 204
take LCM
y ₊ 2y ₊ 3y = 408
6y = 408
y = 408/6
y = 68
hence the number of daffodils is 68.
now substitute y value in x = y/2
x = 68/2
x = 34
now substitute x value in z= 3x
z = 3(34)
z = 102
hence we get the number of tulips,daffodils and hyacinths as 34 , 68 and 102 respectively.
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