How many boxes of each are in the order?

Question

Ace Hardware sells boxes of wrenches ($127) and hammers ($334). Howard ordered 37 boxes of wrenches and hammers for $9,667. How many boxes of each are in the order?

Answer 1

assume number of wrench boxes to be w and number of hammer boxes to be h

this is a 2 equations in 2 unknowns problem

equation 1

w+h = 37

equation 2

127w+334h = 9667

 

from equation 1, w = 37-h

substitute in equation 2

127(37-h)+334h = 9667

4699 - 127h + 334h = 9667

207h  = 4968

h = 24 boxes

w = 13 boxes

Answer 2

let's say Ace sells x boxes of wrenches and (37 - x) boxes of hammers

we have the following equation:

 

127x + 334(37 - x) = 9667

127x + 12,358 - 334x = 9667

-207x = -2691

x = 13

 

Ace sells 13 boxes of wrenches and 37 - 13 = 24 boxes of hammers