A box of candies contains caramel chocolates and chocolates with nuts. If there are 3 times as many caramel chocolates, what is the number of each type if the total is 20?

To solve the problem, we first need to define the variables for the types of chocolates. Let the number of chocolates with nuts be represented as ( x ). Since there are 3 times as many caramel chocolates, we can express the number of caramel chocolates as ( 3x ).

The total number of chocolates is given as 20, which leads to the equation:

[

3x + x = 20

]

This simplifies to:

[

4x = 20

]

Dividing both sides by 4 gives:

[

x = 5

]

Now, substituting ( x ) back into our expressions for the number of chocolates, we find:

• The number of chocolates with nuts is ( x = 5 ).

• The number of caramel chocolates is ( 3x = 3 \times 5 = 15 ).

Thus, the correct quantities are 15 caramel chocolates and 5 chocolates with nuts.

This reasoning shows that the correct answer reflects the condition of having three times as many caramel chocolates compared to nuts, while also ensuring the total adds up to 20. The context of the problem is based on simple algebraic representation and solutions, which effectively shows how to reach