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 you each collect?

Answer 1

I collect 1 rock and 24 fossils

Friend collects 3 rocks and 12 fossils

Explanation:

Let the rock be X and Fossils be Y

Friends collect 3 times rock= 3X and half as many fossils=y/2

Total object i collect= 25

Total object friend collect= 15

Using simultaneous equation

X+Y= 25 eqn 1

3X + Y/2= 15 equation 2

Using substitution method

X=25-Y from eqn 1

Substitute for X in eqn 2

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

75-3y+y/2=15

find the LCM and solve

150-6y+y=30

150-5y=30

collect like terms

-5y=30-150

-5y=-120

Y=24

Find the value of x using eqn 1 by substituting for the value of the gotten Y

X + Y= 25

X + 24= 25

X= 25-24

X=1

Since X stand for rock and Y stand for Fossils, we slot the values into the equation

I collect 1 rock and 24 fossils

While my friend collect 3 rock and 12 fossils