Question

You and your friend each collect rocks and fossils. Your friend collects three times as many rocks and half as many fossils as you. You collect 25 objects. Your friend collects 15 objects. How many rocks and how many fossils do each collect

Answer 1

You collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.

Step-by-step explanation:

Let's assign variables to represent the number of rocks and fossils that you and your friend collect.

Let x represent the number of rocks you collect.

Since your friend collects three times as many rocks as you, we can represent the number of rocks your friend collects as 3x.

Let y represent the number of fossils you collect.

Since your friend collects half as many fossils as you, we can represent the number of fossils your friend collects as y/2.

From the information given, we know that you collect 25 objects, so we have the equation:

x + y = 25

We also know that your friend collects 15 objects, so we have the equation:

3x + y/2 = 15

Simplifying the second equation by multiplying both sides by 2, we get:

6x + y = 30

We now have a system of equations:

x + y = 25

6x + y = 30

Solving this system of equations, we can subtract the first equation from the second equation to eliminate y:

(6x + y) - (x + y) = 30 - 25

5x = 5

x = 1

Substituting the value of x into the first equation, we find:

1 + y = 25

y = 24

Therefore, you collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.

Answer 2

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

`3x + y((1)/(2)) = 15`

`3x + ((y)/(2)) = 15`-------------------(2)

Substituting (1) in (2)

`3(25 -y) + ((y)/(2)) = 15`

`75 - 3y + ((y)/(2)) = 15`

Grouping the like terms we get,

`75 - 15 = 3y - ((y)/(2))`

`60= (6y-y)/(2))`

`60 * 2= 6y-y`

`120= 5y`

`y = (120)/(5)`

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

`(y)/(2) = (24)/(2) =12 fossils`