Question

Maddie has 180 coins. Of these coins \[\dfrac{1}{12}\] are dimes. About how many dimes does she have?

Answer 1

Hint: This type of problem is based on the concept of solving linear equations. First, we have to assume that x is the total number of dimes Maddie has. We then have to find \[\dfrac{1}{12}\] of 180. Equate both and we get a linear equation with one variable. Then solve the obtained equation and find the value of x. Thus, we get the total number of dimes Maddie has.

Complete step by step solution:
According to the question, we are asked to find the total number of dimes.
We have been given the total number of coins is 180.
Let us first assume x to be the total number of dimes Maddie have.
Given in the question, \[\dfrac{1}{12}\] of 180 coins are dimes.
That is, \[180\times \dfrac{1}{12}\] are dimes.
But we have assumed that x as the total number of dimes Maddie has.
Therefore,
\[x=180\times \dfrac{1}{12}\]
On further simplification, we get
\[x=\dfrac{6\times 30}{6\times 2}\]
\[\Rightarrow x=\dfrac{30}{2}\]
\[\therefore x=15\]
 Therefore, the total number of dimes is 15.

Hence, the total number of dimes Maddie has out of 180 coins is 15.

Note: Whenever you get this type of problem, we should always try to make the necessary calculations in the given conditions to get the final of x which will be the required answer. We should avoid calculation mistakes based on sign conventions. We can also solve this question without substituting x. Here \[180\times \dfrac{1}{12}\] can be directly solved. This method can be used to reduce the number of steps.