During a sale, 6 necklaces and 11 rings cost $823. If Tina bought 14 necklaces and 11 rings, she would have spent all her money. Each necklace cost $55 more than a ring. Find the amount that Tina had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
6 |
11 |
14 |
11 |
| Value |
1 u + 55 |
1 u |
1 u + 55 |
1 u |
| Total value |
6 u + 330 |
11 u |
14 u + 770 |
11 u |
Cost of 1 ring = 1 u
Cost of 11 rings = 11 u
Cost of 1 necklace = 1 u + 55
Cost of 6 necklaces = 6 x (1 u + 55) = 6 u + 330
Total cost of 11 rings and 6 necklaces
= 11 u + 6 u + 330
= 17 u + 330
17 u + 330 = 823
17 u = 823 - 330
17 u = 493
1 u = 493 ÷ 17 = 29
Cost of 14 necklaces = 14(1 u + 55) = 14 u + 770
Cost of 11 rings = 11 u
Amount that Tina had at first
= 14 u + 770 + 11 u
= 25 u + 770
= 25 x 29 + 770
= $1495
Answer(s): $1495
