During a sale, 3 necklaces and 9 rings cost $1446. If Opal bought 7 necklaces and 3 rings, she would have spent all her money. Each necklace cost $122 more than a ring. Find the amount that Opal had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
3 |
9 |
7 |
3 |
| Value |
1 u + 122 |
1 u |
1 u + 122 |
1 u |
| Total value |
3 u + 366 |
9 u |
7 u + 854 |
3 u |
Cost of 1 ring = 1 u
Cost of 9 rings = 9 u
Cost of 1 necklace = 1 u + 122
Cost of 3 necklaces = 3 x (1 u + 122) = 3 u + 366
Total cost of 9 rings and 3 necklaces
= 9 u + 3 u + 366
= 12 u + 366
12 u + 366 = 1446
12 u = 1446 - 366
12 u = 1080
1 u = 1080 ÷ 12 = 90
Cost of 7 necklaces = 7(1 u + 122) = 7 u + 854
Cost of 3 rings = 3 u
Amount that Opal had at first
= 7 u + 854 + 3 u
= 10 u + 854
= 10 x 90 + 854
= $1754
Answer(s): $1754
