Question

*2. Formulate the number of daisies varied inversely as the number of sunflowers

Answer 1

There are 260 sunflowers  when there were 5 daisies and 100 roses

Given :

the number of daisies varied inversely as the number of sunflowers and directly as the number of roses.

Let 'd' be the daisies  and 's' be the sunflowers  and 'r' be the roses

Daises varies inversely as sunflowers and directly as roses

So, the equation becomes $d=\frac{k(r)}{s}$

where k is the constant

Lets find out 'k' using the given information

When there 65 daisies, there were 15 roses and 3 sunflowers

d=65, r=154 and s=3. Replace the values and find out k

$d=\frac{k(r)}{s}\\65=\frac{k(15)}{3} \\65=5k\\Divide \; by \; 5\\k=13$

Replace k with 13 in the equation

$d=\frac{k(r)}{s}\\d=\frac{13(r)}{s}$

Now we find out number of sunflowers using the above equation

d=5  and r=100 . Replace the values and find out 's'

$d=\frac{13(r)}{s}\\5=\frac{13(100)}{s}\\5=\frac{1300}{s} \\multiply \; by \; s\\5s=1300\\divide \; by \; 5\\s=260$

There are 260 sunflowers  when there were 5 daisies and 100 roses

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