Question

DeSean is Sorting his rock collection. 2/3 of the rocks are metamorphic, and 3/4 of the remainder are igneous rocks. If the 3 rocks left over are sedimentary, how many rocks does DeSean have?

Answer 1

DeSean has 36 rocks

Further explanation  

Fraction numbers are known as numerator and denominator  

On a number line, fractions are expressed in points that lie between two integers  

The general form of fractions is  

$\large{\boxed{\bold{\frac{a}{b}} }$  

a = numerator  

b = denominator  

Mixed fractions consist of whole number and ordinary fractions  

There are a number of steps in adding fraction operations

• 1. the denominators must be the same, if not then  

a. Multiply top and bottom of each fraction by the denominator of the other. or  

b. we can use Least Common Denominator is  

the smallest of all the common denominators.  

• 2: Add the numerators and put over the denominator  

• 3: Simplify the fraction

DeSean is Sorting his rock collection $\frac{2}{3}$ are metamorphic,   $\frac{3}{4}$ of the remainder are igneous rock and 3 rocks left over are sedimentary

Let x = total rock

• $\frac{2}{3}$ are metamorphic

we translate this sentence into equation

$\displaystyle metamorphic=\frac{2}{3}x$,

• $\frac{3}{4}$ of the remainder are igneous rock

we translate this sentence into equation

$\displaystyle igneous rock=\frac{3}{4}\times\frac{1}{3}x$,

so total of Dean's rock:

$\displaystyle x=\frac{2}{3}x+\frac{3}{4}\times\frac{1}{3}x +3$

Because the denominator is not the same, so we can use both multiplying or least common denominator.

let we use least common denominator:

List multiples of 3: 3, 6, 9, 12, 15, 18, 21...

List multiples of 12: 12,24,36 ...  

the smallest number that is the same: = 12

then addition operation becomes :

$\displaystyle x=\frac{8}{12}x+\frac{3}{12}x +3$

$\displaystyle x=\frac{11}{12}x+3$

$\displaystyle \frac{1}{12}x=3$

$\displaystyle \large{\boxed{\bold{x=36}}}$

Learn more  

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Keywords : rock collection, fractions addition,metamorphic,igneous rocks

Answer 2

2/3 of the rocks are metamorphic
3/4 of the remainder are igneous rocks
3 rocks left over are sedimentary

the rocks that deSean has are
2/3+3/4+3= 4x2+3x3/3x4     + 3  = 17+36 /12 = 20
DeSean had 20 rocks