Answer:
Number of rocks and fossils collected by you is 1 and 24 respectively
Number of rocks and fossils collected by your friend is 3 and 12 respectively
Step-by-step explanation:
Let the number of Rocks you collect be x
Let the number of Fossils you collect be y
Then the total number pf objects you collected will be
x + y = 25
x = 25 - y------------------------------(1)
Your friend collects three times as many rocks and half as many fossils as you.
This can be written as
[tex]3x + y(\frac{1}{2}) = 15[/tex]
[tex]3x + (\frac{y}{2}) = 15[/tex]-------------------(2)
Substituting (1) in (2)
[tex]3(25 -y) + (\frac{y}{2}) = 15[/tex]
[tex] 75 - 3y + (\frac{y}{2}) = 15[/tex]
Grouping the like terms we get,
[tex] 75 - 15 = 3y - (\frac{y}{2})[/tex]
[tex] 60= \frac{6y-y}{2})[/tex]
[tex] 60 \times 2= 6y-y[/tex]
[tex] 120= 5y[/tex]
[tex] y = \frac{120}{5}[/tex]
y= 24
Substituting y value in equation(1) we get
x = 25 - 24
x= 1
Friends collects 3 times rock
so collects 3x =3(1) = 3rocks
Also he collects half as many fossils
That is
[tex]\frac{y}{2} = \frac{24}{2} =12 fossils[/tex]
