Rick has 150 fewer stamps than Myra. Together they have collected 500. How many stamps does each person have in his or her collection?

Question

Don't know how to show my son how to set up the problem so he can solve it. 

Answer 1

(1) First, we know a total: 500 stamps. So, one side of the equation will look like this: =500 stamps. Whatever Rick and Myra collected together will equal 500 total stamps.

 

Myra's stamps + Rick's stamps = 500 stamps

 

 

 

(2) Who has more stamps? Rick or Myra? Myra does. So we must subtract 150 stamps from Myra's stamps to see how many Rick has.

 

Myra's stamps + (Myra's stamps - 150 stamps) = 500 stamps

 

 

 

(3) If we were to use the letter S for stamps to make things simpler, we could rewrite our equation to look like this:

 

S + (S - 150) = 500

 

 

 

(4) Since we are only adding and subtracting, the parenthesis are not important:

 

S + S - 150 = 500

 

Now we can solve.

 

 

 

(5) Add 150 to both sides:

 

S + S - 150 + 150 = 500 + 150

 

 

 

(6) Simplify:

 

S + S = 650

 

 

 

(7) S + S must mean that each S added together equals 650. There are 2 Ss so let's divide 650 by two.

 

 

2S / 2 = 650 / 2

 

 

 

(8) Now we are left with:

 

S = 325

 

Myra has 325 stamps.

 

 

 

(9) Well, how many did Rick have?

 

Oh yea: "Myra's stamps - 150".

 

325 - 150 = 175 stamps.

 

Myra = 325 stamps

Rick = 175 stamps

 

 

 

To double check, let's see if together we have 500 stamps:

 

325 stamps + 175 stamps = 500 total stamps :)

 

 

 

I hope this answer helps. Let me know if you have any questions.

Answer 2

Myra has some number of stamps.  Call it M (for Myra).  

Rick also has some number of stamps.  Call it R (for Rick).  

 

"Rick has 150 fewer stamps than Myra".  This means that R is 150 less than M, or as an equation, R = M - 150.  

"Together they have collected 500".  This means that R plus M is equal to 500, or R + M = 500.  

 

Since R is equal to M - 150 you can replace the R in the second equation with M - 150 to get (M - 150) + M = 500.  

Combine like terms (M + M = 2M) to get 2M - 150 = 500.  

Add 150 to both sides of the equation to get 2M = 650.  

Divide both sides of the equation by 2 to get M = 325, which is the number of stamps Myra has.  

 

Since R = M - 150, Rick has 325 - 150 = 175 stamps.  

 

To check the answer, note that 325 + 175 = 500 stamps total, and 325 - 150 = 175, so Rick has 150 fewer stamps then Myra.