Question

If the ratio of number of apples to number of oranges in a box is 3:8, then the number of apples and oranges in the box can be _______

• A. Apples = 24 ; Oranges = 9
• B. Apples = 9 ; Oranges = 24
• C. Apples = 33 ; Oranges = 77
• D. Apples = 3 ; Oranges = 11

Answer 1

The correct option is B Apples = 9 ; Oranges = 24

$\text{Calculating the ratio between the number}\text{of apples and oranges in each case, we}\text{find:}$

$Case1:$

$\text{Apples = 24 ; Oranges = 9}$

$\text{Fraction of apples to oranges}=\frac{24}{9}=\frac{24÷3}{9÷3}=\frac{8}{3}$

$\text{Representing the fraction as a ratio,}\text{we find:}$

$\frac{8}{3}⟹8:3$


$Case2:$

$\text{Apples = 9 ; Oranges = 24}$

$\text{Fraction of apples to oranges}=\frac{9}{24}=\frac{9÷3}{24÷3}=\frac{3}{8}$

$\text{Representing the fraction as a ratio,}\text{we find:}$

$\frac{3}{8}⟹3:8$


$Case3:$

$\text{Apples = 33 ; Oranges = 77}$

$\text{Fraction of apples to oranges}=\frac{33}{77}=\frac{33÷11}{77÷11}=\frac{3}{7}$

$\text{Representing the fraction as a ratio,}\text{we find:}$

$\frac{3}{7}⟹3:7$


$Case4:$

$\text{Apples = 3 ; Oranges = 11}$

$\text{Fraction of apples to oranges}=\frac{3}{11}$

$\text{Representing the fraction as a ratio,}\text{we find:}$

$\frac{3}{11}⟹3:11$

$\text{The given ratio of number of apples to}$
$\text{numebr of oranges is}\text{3:8}$

$\therefore \text{The distribution of fruits in the box}$ $\text{can be:}$

$\text{Apples = 9 ; Oranges = 24}$