One-Up Games just started selling a new game console for $300 and games for the new console for $50 each. The store set a sales goal of $7,000 for Saturday and Sunday combined. Unfortunately, the store gets only 10 consoles per day from the manufacturer due to high demand.
Which pairs (c,g) represent possible numbers of consoles and games that would allow the store to meet its weekend sales goal?
The possible pairs (c,g) representing numbers of consoles and games that would allow the store to meet its weekend sales goal of $7,000 are those that satisfy the equation:
300c + 50g = 7000
Given that the store can only get 10 consoles per day, the total number of consoles for the weekend (c) is limited to 10*2 = 20. Let's examine the possible pairs:
1. (0, 140) - not possible as there must be at least 1 console sold
2. (1, 130) - possible, as 300*1 + 50*130 = $6,500
3. (2, 120) - not possible, as 300*2 + 50*120 = $6,600
4. (3, 110) - not possible, as 300 *3 + 50*110 = $6,900
5. (4, 100) - possible, as 300*4 + 50*100 = $7,000
6. (5, 90) - not possible, as 300*5 + 50*90 = $7,500
7. (6, 80) - not possible, as 300*6 + 50*80 = $8,100
8. (7, 70) - not possible, as 300*7 + 50*70 = $8,100
9. (8, 60) - not possible, as 300*8 + 50*60 = $8,400
10. (9, 50) - not possible, as 300*9 + 50*50 = $8,400
11. (10, 40) - not possible, as 300*10 + 50*40 = $8,500
12. (10, 30) - not possible, as 300*10 + 50*30 = $8,000
13. (10, 20) - not possible, as 300*10 + 50*20 = $7,500
14. (10, 10) - not possible, as 300*10 + 50*10 = $7,000
15. (10, 0) - not possible, as there must be at least 1 game sold
So the possible pairs (c,g) representing numbers of consoles and games that would allow the store to meet its weekend sales goal of $7,000 are:
- (1, 130)
- (4, 100)