Answer:
I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.
Step-by-step explanation:
The number of total objects collected by me = 20
The number of objects collected by my friend = 20
Let us assume:
The number of rocks collected by me = m
The number of fossils collected by me = 2 k
⇒ m + 2 k = 20 .... (1)
So, according to the question:
The number of rocks collected by my friend = 3 x (rocks collected by me)
= 3 x (m) = 3 m
The number of fossils collected by my friend = 1/2 x (fossils collected by me) = 1/2 x (2k ) = k
⇒ 3 m + k = 20 .... (2)
Solving (1)and (2) for the value of m and k, we get:
m + 2 k = 20 ⇒ m = 20 - 2 k ... Put this in (2)
3 m + k = 20 ⇒ 3 (20 - 2 k) + k = 20
⇒ 60 - 6 k + k = 20
or, - 5k = -40
or, k = 40/5 = 8
⇒ k= 8
m + 2(8) = 20
or, m = 4
Hence, the number of rocks collected by me = m = 4
The number of fossils collected by me = 2 k = 2 (4) = 16
Hence, the number of rocks collected by my friend = 3 m = 3 x 4 = 12
The number of fossils collected by my friend = k = 8
Hence, I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.
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