During a sale, 8 rings and 3 necklaces cost $1380. If Anna bought 15 rings and 13 necklaces, she would have spent all her money. Each ring cost $145 more than a necklace. Find the amount that Anna had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Necklaces |
Rings |
Necklaces |
| Number |
8 |
3 |
15 |
13 |
| Value |
1 u + 145 |
1 u |
1 u + 145 |
1 u |
| Total value |
8 u + 1160 |
3 u |
15 u + 2175 |
13 u |
Cost of 1 necklace = 1 u
Cost of 3 necklaces = 3 u
Cost of 1 ring = 1 u + 145
Cost of 8 rings = 8 x (1 u + 145) = 8 u + 1160
Total cost of 3 necklaces and 8 rings
= 3 u + 8 u + 1160
= 11 u + 1160
11 u + 1160 = 1380
11 u = 1380 - 1160
11 u = 220
1 u = 220 ÷ 11 = 20
Cost of 15 rings = 15(1 u + 145) = 15 u + 2175
Cost of 13 necklaces = 13 u
Amount that Anna had at first
= 15 u + 2175 + 13 u
= 28 u + 2175
= 28 x 20 + 2175
= $2735
Answer(s): $2735
