Math Word Problem

Question

Suppose that a turkey from Gelson's costs 15 cents more per pound than a turkey from Ralphs and a turkey from Ralphs costs 8 cents more per pound than a turkey from Albertson's. Then, if you buy two 16-pound turkeys from Albertson's, one 19-pound turkey from Ralph's and one 18-pound turkey from Gelson's you'd pay $125.03. Find the price per pound for a turkey from Gelson's.

Answer 1

First, assign some variables:

 

let r = the price per pound from Ralphs

let g = the price per pound from Gelson's

let a = the price per pound from Albertson's

 

The first part of the problem is relating the price per pound from each store.  They are:

 

g = r + 15

r = a + 8

 

Substituting r into g also lets us express g in terms of a,

 

g = a + 23

 

We have two equations with three unknowns.  The last part of the problem provides the third equation.  This equation is:

 

32*a + 19*r + 18*g = 12503   

 

Remember, we have to have consistent units.  The left hand side of the equation and our two equations above are in cents so the right hand side must also and $125.03 = 12503 cents.

 

Since we ultimately want the price from Gelson's, let's put the last equation in terms of g. We can do this using the relations from the first part of the problem,

 

32*(g - 23) + 19*(g - 15) + 18*g = 12503.

 

Solving this expression for g gives g = 196.  Remember this is in cents, so to convert to dollars divide by 100.  This gives us the price per pound of turkey from Gelson's.  That is, $1.96 per pound.