During a sale, 6 necklaces and 3 rings cost $585. If Sarah bought 9 necklaces and 7 rings, she would have spent all her money. Each necklace cost $78 more than a ring. Find the amount that Sarah had at first.
|
Case 1 |
Case 2 |
|
Necklaces |
Rings |
Necklaces |
Rings |
Number |
6 |
3 |
9 |
7 |
Value |
1 u + 78 |
1 u |
1 u + 78 |
1 u |
Total value |
6 u + 468 |
3 u |
9 u + 702 |
7 u |
Cost of 1 ring = 1 u
Cost of 3 rings = 3 u
Cost of 1 necklace = 1 u + 78
Cost of 6 necklaces = 6 x (1 u + 78) = 6 u + 468
Total cost of 3 rings and 6 necklaces
= 3 u + 6 u + 468
= 9 u + 468
9 u + 468 = 585
9 u = 585 - 468
9 u = 117
1 u = 117 ÷ 9 = 13
Cost of 9 necklaces = 9(1 u + 78) = 9 u + 702
Cost of 7 rings = 7 u
Amount that Sarah had at first
= 9 u + 702 + 7 u
= 16 u + 702
= 16 x 13 + 702
= $910
Answer(s): $910