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# Three students share a bag of garri in such a way that the first student took $$\frac{1}{4}$$ of the garri and the second $$\frac{3}{4}$$ of the remainder. What fraction of ...

### Question

Three students share a bag of garri in such a way that the first student took $$\frac{1}{4}$$ of the garri and the second $$\frac{3}{4}$$ of the remainder. What fraction of the bag of garri did the third student take?

### Options

A)
$$\frac{3}{16}$$
B)
$$\frac{2}{9}$$
C)
$$\frac{3}{5}$$
D)
$$\frac{4}{15}$$

### Explanation:

To understand this question, you need to know the concept of fractions and how they are divided or subtracted from a whole. Here, a bag of garri is considered as 1 whole.

The first student took $$\frac{1}{4}$$ of the garri. That means he took one-fourth of the entire bag, leaving behind three-fourths or $$\frac{3}{4}$$ of the bag.

The second student took $$\frac{3}{4}$$ of the remaining garri. To calculate the amount the second student took, we multiply the fractions. So, $$\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$$.

The third student took the rest of the garri that was left after the first and second students took their shares. To calculate the amount the third student took, we subtract the fractions of the garri taken by the first and second students from 1 (the total amount).

So, the third student took $$1 - \frac{1}{4} - \frac{9}{16} = 1 - \frac{4}{16} - \frac{9}{16} = 1 - \frac{13}{16} = \frac{3}{16}$$.

Therefore, the third student took $$\frac{3}{16}$$ of the bag of garri, which is Option A.

## Dicussion (1)

• Alatise Paul

Student 1=1/4, student 2 =3/4x(1-1/4)=
3/4=9/16
Student 3=x
1/4+x+9/16=1
1/4+9/16+x=1
4+9/16
13/16+x=1
X=1-13/16
16-3/16