Question

Sara has caramel and orange-flavored candies. The number of caramel candies is one-third the number of orange-flavored candies. If she has 100 candies in total, the number of caramel candies is _______.

• A. 65
• B. 55
• C. 25
• D. 75

Answer 1

The correct option is C 25

Let the number of orange-flavored candies be $x$.
Number of caramel candies $=\frac{1}{3}x$
Number of caramel and orange-flavored candies = 100
$\Rightarrow x+\frac{1}{3}x=100$
$\Rightarrow \frac{x}{1}+\frac{1}{3}x=100$
$\Rightarrow \frac{3x}{3}+\frac{1x}{3}=100$
$\Rightarrow \frac{4x}{3}=100$
$\Rightarrow \frac{4x}{3}\times 3=100\times 3$ [Multiplying both sides by 3]
$\Rightarrow 4x=300$
$\Rightarrow \frac{4x}{4}=\frac{300}{4}$ [Dividing both sides by 4]
$\Rightarrow x=75$
Number of orange-flavored candies = $x$ = 75
Number of caramel candies $=\frac{1}{3}\times x=\frac{1}{3}\times 75=25$