Answer :
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 [tex]d=\frac{k(r)}{s}[/tex]
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
[tex]d=\frac{k(r)}{s}\\65=\frac{k(15)}{3} \\65=5k\\Divide \; by \; 5\\k=13[/tex]
Replace k with 13 in the equation
[tex]d=\frac{k(r)}{s}\\d=\frac{13(r)}{s}[/tex]
Now we find out number of sunflowers using the above equation
d=5 and r=100 . Replace the values and find out 's'
[tex]d=\frac{13(r)}{s}\\5=\frac{13(100)}{s}\\5=\frac{1300}{s} \\multiply \; by \; s\\5s=1300\\divide \; by \; 5\\s=260[/tex]
There are 260 sunflowers when there were 5 daisies and 100 roses
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