Question

Flori’s Flower shop contains fewer than 150 flowers. All the flowers are purple, yellow, red or white. The ratio of purple flowers to yellow flowers is 1 : 2, the ratio of yellow flowers to red flowers is 3 : 4 and the ratio of red flowers to white flowers is 5 : 6. How many flowers are there in Flori’s shop?

Answer 1

Flori's Flower Shop have 48 white flowers, 40 red flowers, 30 yellow flowers and 15 purple flowers, whose sum equals 133 flowers, which is fewer than 150 flowers.

How to determine the quantity of flowers in a flower shop

Flori's Flower shop owns a quantity less than 150 flowers, in which there are four kinds of flowers according to color: (purple - p, yellow - y, red - r, white - w), each variable represents positive integers. Now we proceed to construct the system of equation that describes the situation:

z < 150     (1)

p + y + r + w = z    (2)

p = y/2     (3)

y = 3 · r/4     (4)

r = 5 · w/6     (5)

By (1) and (3) in (2):

y/2 + y + r + w < 150

By (4):

3 · y/2 + r + w < 150

9 · r/8 + r + w < 150

17 · r/8 + w < 150

By (5):

85 · w/48 + w < 150

133 · w/48 < 150

133 · w < 7200

w < 54.135

Now we assume that w = 48, then we have the following solution for the flower shop: r = 40, y = 30, p = 15.

Flori's Flower Shop have 48 white flowers, 40 red flowers, 30 yellow flowers and 15 purple flowers, whose sum equals 133 flowers, which is fewer than 150 flowers. $\blacksquare$

To learn more on inequalities, we kindly invite to check this verified question: brainly.com/question/20383699