Question

Desean is sorting his rock collection. 1/2 of the rocks are metamorphic and 3/4 of the remaining are igneous rocks. If 3 rocks left our are sedimentary. How many rocks does Desean have?

Answer 1

Answer: 24

Step-by-step explanation:

3*4=12

12*2=24

If 3/4 of the remaining rocks are igneous, then you would only have three rocks left. You take the denominator of the 3/4, so 4, and multiply it by 4 to get what one half of the overall amount of rocks are. You then multiply it by 2, getting the answer 24. Hope this helped.

Answer 2

Let's start with the given information:

1/2 of the rocks are metamorphic
The remaining rocks are divided into 2 groups: igneous and sedimentary
3/4 of the remaining rocks (after the metamorphic rocks have been counted) are igneous
3 rocks are sedimentary
Let's use algebra to solve for the total number of rocks that Desean has:

Let x be the total number of rocks that Desean has.

1/2x are metamorphic rocks
The remaining number of rocks is 1/2x.
3/4 of the remaining rocks are igneous: / 3/4(1/2x) = 3/8x are igneous rocks.
3 rocks are sedimentary.
Therefore, the total number of rocks is: x = 1/2x + 3/8x + 3
Simplifying the equation: 8/8x = 4/8x + 3
Combining like terms: 4/8x = 3
Solving for x: x = 3/(4/8) = 6

Therefore, Desean has 6 rocks in total.