Question

In a patriotic bag of red, white and blue M&Ms, it is found that there are 305 M&Ms. There are three times as many red as white. The blue are five more than twice the white. How many blue M&Ms are in the package ?

Answer 1

`105`

Step-by-step explanation

Let the number of red ones be r.

Let the number of white ones be w.

Let the number of blue ones be b.

There are 305 M&Ms in the bag. This means that:

`r+w+b=305`

There are three times as many red as white. This means that:

`r=3w`

The blue are five more than twice the white. This means that:

`b=5+2w`

We can substitute these into the first equation:

`3w+w+5+2w=305`

Solve for w:

`\begin{gathered} 3w+w+2w=305-5 \\ 6w=300 \\ w=(300)/(6) \\ w=50 \end{gathered}`

To find how many blue M&Ms are there, substitute the value of w into the equation for b:

`\begin{gathered} b=5+2(50)=5+100 \\ b=105 \end{gathered}`

That is the number of blue M&Ms in the package.