Question

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?

Answer 1

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.

Answer 2

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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