problem solving

Question

jen, jane and gina buy an 18" mega sub to share. Jen cuts the sandwich such that she gets the largest piece. Jane's piece is only half the size of Jen's, and gina's portion is three-fourths the size of Jen's. How long is each person's part of the sub?

Answer 1

Rocio,

 

Let the size of Jen's portion be x.  Then Jane's piece, y,  is: 

 

(1) y = (1/2)x

 

Gina's portion, z, is:

 

(2) z = (3/4)x

 

We also know that if you add all the portions together, the total is 18 inches:

 

(3) x + y + z = 18

 

Now, substitute the values for y and z in (1) and (2) for y and z in (3):

 

x+ (1/2)x + (3/4)x = 18

 

Simplify (you can use the fractions or multiply everything by the LCD to get rid of the fractions):

 

Multiply everything by 4:

 

4x + 2x + 3x = 72

 

9x = 72 

 

x = 8 inches (Jen's portion)

 

Jane's is (1/2)8 = 4 inches

 

Gina's is (3/4)8 = 6 inches

 

Does this work?

 

8 + 4 + 6 = 18

 

Yep