Keynes Company sells both radios and CD players. The following information is
available with regard to these products:
 
Selling price: Radios:$40, CD players: $70
Unit variable cost: Radios 35, CD players:  50
Unit contribution margin: Radios 5, CD players:  20
Sales mix: Radios 2, CD players:  1
What is the number of radios and CD players that Keynes must sell in
order to breakeven
if fixed costs are $45,000?
Radios CD players
a. 1,000 500
b. 1,500 750
c. 2,000 1,000
d. 3,000 1,500

Step by step solution.  (You can do this much faster.)

Let R = number of radios and C = number of CDs

(R * Price per unit)+ (C * Price per unit) < -- Total revenue

(R * Cost per unit)+ (C * Cost per unit)+ 45,000 < -- Total cost

Total revenue - Total cost = 0  <-- break even condition

[(R * Price)+ (C * Price)] - [(R * Cost)+ (C * Cost)+ 45,000 ] = 0

==> (40R + 70C) - (35R + 50C + 45,000) = 0

==> (40R + 70C - 35R - 50C - 45,000) = 0

==> 5R + 20C = 45,000 <-- break even condition (you could have started
at this point)

But R = 2*C  <-- sales ratio

==> 10c + 20C = 45,000 

==> c = 1,500 

==> R = 3,000

so answer is (d)