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3 years ago

12

You and your friend each collect rocks and fossils. Your friend collects three times as many rocks and half as many fossils as y

ou. You collect 20 objects. Your friend collects 20 objects. How many rocks and how many fossils do you each collect?

1 answer:

pochemuha3 years ago

4 0

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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Read 2 more answers