Question

The ratio of the number of roses to the number of lilies in a flower shop is 3:5. One-sixth of the roses and half of the lilies are white. If there are a total of 24 white flowers, how many lilies are in the flower shop?

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Answer 1

The number of lilies in the flower shop is 40

The number of roses in the flower shop is 24

Explanation:

The ratio of the number of roses to the umber of lilies = 3:5

The number of white roses = 1/6 of the roses

The number of white lilies = half (1/2) of the lilies

The total number of white flowers = 24

Let the number of lilies in the flower shop = L, and the number of roses in the flower shop = R

1/6 × R + 1/2 × L = 24...(1)

R:L = 3:5

R/(R + L) = 3/(3 + 5) = 3/8

3 × (R + L) = 8 × R

3·R + 3·L = 8·R

3·L = 8·R - 3·R = 5·R

3·L = 5·R

L = 5/3·R

Substituting the value of L in equation (1) gives;

1/6 × R + 1/2 × (5/3·R) = 24

1/6 × R + 5/6 × R = 24

(1/6 + 5/6) × R = 24

1 × R = 24

∴ R = 24

L = 5/3·R = 5/3 × R = 5/3 × 24 = 40

L = 40

The number of lilies in the flower shop = L = 40

The number of roses in the flower shop = R = 24.