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

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

$3x + y(\frac{1}{2}) = 15$

$3x + (\frac{y}{2}) = 15$-------------------(2)

Substituting (1) in (2)

$3(25 -y) + (\frac{y}{2}) = 15$

$75 - 3y + (\frac{y}{2}) = 15$

Grouping the like terms we get,

$75 - 15 = 3y - (\frac{y}{2})$

$60= \frac{6y-y}{2})$

$60 \times 2= 6y-y$

$120= 5y$

$y = \frac{120}{5}$

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

$\frac{y}{2} = \frac{24}{2} =12 fossils$