Algebraic expressions and word problems

Question

Rafael, Hector and Brian are comparing stamp collections. Hector has 50 more stamps than Rafael has. Brian has one-half the stamps that Hector has. Let s represent the number of stamps Rafael has. If Brian has 100 stamps calculate the number of stamps they have all together if Brian has 100 stamps.

Answer 1

Does Brian have 100 stamps?

 

If Rafael has s stamps, then Hector has s + 50 stamps, right? We know he has 200, so...

 

s + 50 = 200

         s = 150

 

In total, they have 100 + 200 + 150 = 450 stamps.

 

Hope this helps!

 

 

Answer 2

Hi Erin.

 

Take this one statement at a time...

 

The first sentence is worthless.  Cross it out.

 

 

 

Hector = 50 + Rafael  (2nd sentence)

 

Brian = (1/2)(Hector)    (3rd sentence)

 

 

 

Replace "Rafael" with "s"  (4th sentence)

 

 

 

This results in:

 

Hector = 50 + s

Brian = (1/2)(Hector) = (1/2)(50 + s)

 

 

Brian has 100 stamps.  So replace "Brian" with 100

 

100 = (1/2)(50 + s)  <--  Solve this.

 

Mult both side by 2

 

200 = 50 + s

 

Subtract 50 from both sides

 

150 = s

 

Remember, "s" is the number of stamps Rafael has, so determine the other's stamp numbers from this.

 

Rafael has 150 stamps.

Hector has 50 more than Rafael so Hector has 200 stamps.

Brian has half the stamps that Hector has, so Brian has (1/2)(200) = 100 stamps.

 

Final answer:

 

Rafael: 150 stamps

Hector: 200 stamps

Brian: 100 stamps