During a sale, 3 necklaces and 9 rings cost $321. If Jade bought 4 necklaces and 9 rings, she would have spent all her money. Each necklace cost $55 more than a ring. Find the amount that Jade had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
3 |
9 |
4 |
9 |
| Value |
1 u + 55 |
1 u |
1 u + 55 |
1 u |
| Total value |
3 u + 165 |
9 u |
4 u + 220 |
9 u |
Cost of 1 ring = 1 u
Cost of 9 rings = 9 u
Cost of 1 necklace = 1 u + 55
Cost of 3 necklaces = 3 x (1 u + 55) = 3 u + 165
Total cost of 9 rings and 3 necklaces
= 9 u + 3 u + 165
= 12 u + 165
12 u + 165 = 321
12 u = 321 - 165
12 u = 156
1 u = 156 ÷ 12 = 13
Cost of 4 necklaces = 4(1 u + 55) = 4 u + 220
Cost of 9 rings = 9 u
Amount that Jade had at first
= 4 u + 220 + 9 u
= 13 u + 220
= 13 x 13 + 220
= $389
Answer(s): $389
