modeling problems

Question

Last week Michael sold twice as many red high tops as cross trainers. Red high tops sell for $20/pair and a cross trainer sells for $40/pair. He grossed $2000 in sales for the week. Construct a linear system describing the number of cross trainers in terms of the number of red high tops sold last week. 

A) define your input and output variables

B)algebraically construct a 2 by 2 linear system involving your input and output variables. 

Answer 1

r = number of red high tops sold

c = number of cross trainers sold

 

r = 2c

20r + 40c = 2000

 

Using substitution replace r with 2c in equation 2 and solve for c

 

20(2c) + 40c = 2000

40c + 40c = 2000

80c = 2000

c = 25 cross trainers sold

r = 2c = 50 red high tops sold