Can't figure out the correct equation

[seafair]

I was able to figure out the following story problem through a lot of trial and error and finally came up with the answer of 75 and 30, more guesswork than math. Could someone please show me the equation that correctly solves this?

Monica and Marty were given 105 pieces of candy. Monica has 2 1/2 times as much candy as Marty. How many pieces of candy do each have?

 

[Denis]

Let Monica's candies = x; then Marty's candies = 105 - x : got that?

x = 2.5(105 - x) : still with me?

Solve for x

 

[Loren]

I was able to figure out the following story problem through a lot of trial and error and finally came up with the answer of 75 and 30, more guesswork than math. Could someone please show me the equation that correctly solves this?

Monica and Marty were given 105 pieces of candy. Monica has 2 1/2 times as much candy as Marty. How many pieces of candy do each have?

There are more than one approaches to a problem such as this. Here is one approach.

Always name stuff and write it down.

Let x represent the number of pieces of candy that Marty has.
Then the number of pieces that Monica has is represented by 5/2x.
Now, we are told that they were given a total of 105 pieces.
Can that be the basis for a statement of equality?

x + 5/2x = 105

Solve for x.

 

[seafair]

Thank you for the help.