Hannah finds purple, blue, and silver space rocks while exploring. 2/3 of the rocks are purple and 3/4 of the remainder are blue. if there are 3 silver rocks, how many space rocks does hannah have?

To answer this, you will determine what fraction of the original rocks are silver by using the information about the other two colors.

If 2/3 of them area purple, than 1/3 are not.

If 3/4 of the remaining 1/3 is blue, than 3/4 x 1/3 = 3/12 of then are blue.

2/3 are purple, 3/12 of them are blue, the remaining is silver,

1 - 2/3 - 3/12
1 - 8/12 - 3/12 = 1/12

1/12 of the rocks are silver. If 3 are silver, write an equation that needs solved.

1/12r = 3
r = 36 rocks

There were 36 space rocks in total.

The number of space rocks that Hannah has = 36 space rocks

We are told that;

⅔ of the rocks are purple

Fraction left that is not purple = ⅓

¾ of the remaining are blue = ¾ × ⅓ = ¼

Thus;

Fraction that is silver = 1 - (fraction that is purple + fraction that is blue)

Fraction that is silver = 1 - (⅔ + ¼)

Fraction that is silver = 1/12

Since there are 3 silver rocks, then;

(1/12)x = 3

Where x is total number of space rocks.

Thus;

x = 12 × 3

x = 36

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