Write the expressions: [tex]y+p=164
\\ y=3p[/tex]
The variable y represents the number of yellow marbles. The variable p represents the number of purple marbles. The first expression is saying that when we add both the yellow and purple marbles together, there are 164 total. The second expression is saying for every one purple marble, there are three yellow, or that there are three times as many yellow marbles.
Lets find how many purple marbles there are:
First, substitute 3p for y in our first equation. [tex](3p)+p=164[/tex]
Combine like terms. [tex]4p=164[/tex]
Isolate the variable by dividing both sides by 4. [tex]p=41[/tex]
There are 41 purple marbles.
Now, let find how many yellow marbles.
Because we already know there are 41 purple marbles, lets replace p with 41. [tex]y+(41)=164[/tex]
Isolate the variable by subtracting 41 from both sides. [tex]y=123[/tex]
There are 123 yellow marbles.
Now we should check.
Substitute the variables in the first expression. Is it true?
[tex]123+41=164
\\ 164=164[/tex]
Yes, because 41 plus 123 equals 164, it is true.
Substitute the variables in the second expression. Is it true also?
[tex]123=3(41)
\\ 123=123[/tex]
Yes, because 41 times 3 equals 123, it is true.
