Question

There are two types of packing of candies. Each mega (large type) has 20 more candies than the number of candies in 15 packs of smaller type. If each mega type contains 200 candies, find the number of candies in each small box.

Answer 1

Hint:
Here, we need to find the number of candies in each small box. Let the number of candies in each small box be \[x\]. We need to apply the given operations on \[x\] to form a linear equation in terms of \[x\]. Then, we need to solve this equation to find the value of \[x\] and hence, find the number of candies in each small box.

Complete step by step solution:
Let the number of candies in each small box be \[x\].
We need to apply the given operations on the number \[x\] to obtain a linear equation in terms of \[x\].
First, we will multiply the number of candies in 1 small box by 15 to get the number of candies in 15 small boxes.
Therefore, we get the expression
Number of candies in 15 small boxes \[ = 15x\]
Now, we will find the expression for 20 more candies than the number of candies in 15 small boxes.
Adding 20 to the number of candies in 15 small boxes, we get the expression
\[15x + 20\]
Thus, the number of candies in each mega type box is \[15x + 20\].
Now, it is given that the mega type contains 200 candies.
Therefore, we get the equation
\[ \Rightarrow 15x + 20 = 200\]
We need to solve this equation to get the value of \[x\] and hence, find the number of candies in each small box.
Subtracting 20 from both sides of the equation, we get
$ \Rightarrow 15x + 20 - 20 = 200 - 20 \\
   \Rightarrow 15x = 180 \\ $
Dividing both sides of the equation by 15, we get
\[ \Rightarrow \dfrac{{15x}}{{15}} = \dfrac{{180}}{{15}}\]
Thus, we get the value of \[x\] as
\[\therefore x = 12\]
Therefore, we get the number of candies in each small box as 12 candies.
We can verify our answer by applying the stated operations on the number 12.
The number of candies in 15 small boxes is \[15 \times 12 = 180\] candies.
20 more than 180 candies is equal to 200 candies.
This is equal to the given number of candies in each mega type box.
Hence, we have verified our answer.


Note:
We have used the given information to form a linear equation in one variable in terms of \[x\] in the solution. A linear equation in one variable is an equation that can be written in the form \[ax + b = 0\], where \[a\] is not equal to 0, and \[a\] and \[b\] are real numbers. A linear equation of the form \[ax + b = 0\] has only one solution.