According to the information given, we have two equations:
5
D
=
2
P
5D=2P (Five times the number of daisies equals twice the number of prunes)
D
+
P
=
35
D+P=35 (The total number of daisies and prunes is 35)
Now, we can solve these equations simultaneously. From equation 1, we can express
P
P in terms of
D
D:
P
=
5
2
D
P=
2
5
D.
Substituting this into equation 2:
D
+
5
2
D
=
35
D+
2
5
D=35
2
D
+
5
D
=
70
2D+5D=70
7
D
=
70
7D=70
Solving for
D
D, we find
D
=
10
D=10.
Now, using the value of
D
D in equation 2:
10
+
P
=
35
10+P=35
P
=
35
−
10
P=35−10
P
=
25
P=25
So, there are 10 daisies and 25 prunes.