So I'm having an issue with a linear word problem.

Question

So to paraphrase the problem:  I have to mix two types of coffee together, one that is $4 a lb, and another that is $2.40 a lb to create 80lbs of a mix for $3.60 a lb.  The instructor said to try and arrange this as a table to figure out, but I can't get this to add up.

Answer 1

Hi Sean,

Not sure what your instructor means by a table but here is an algebraic solution to your problem.

 

Let x1 be the $4/lb coffee and x2 be the $2.40/lb coffee.

 

x1 + x2 = 80 lbs (the total amount to be produced)

4*x1 + 2.4*x2 = 3.6*80 (the $/lb of 3.6 times the total amount produced)

 

solve first equation for x1 and substitute in second equation for x1 

 

x1 = 80 - x2

 

4*(80-x2) +  2.4 * x2 = 288

-4*x2 + 2.4 * x2 = 288 - 320 = -32 = -1.6 x2

x2 = 20 and x1 = 60

just to verify

60*4+20*2.4 = 288

288/80=3.6

 

hope this helps