During a sale, 4 necklaces and 7 rings cost $412. If Olivia bought 10 necklaces and 3 rings, she would have spent all her money. Each necklace cost $26 more than a ring. Find the amount that Olivia had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
4 |
7 |
10 |
3 |
| Value |
1 u + 26 |
1 u |
1 u + 26 |
1 u |
| Total value |
4 u + 104 |
7 u |
10 u + 260 |
3 u |
Cost of 1 ring = 1 u
Cost of 7 rings = 7 u
Cost of 1 necklace = 1 u + 26
Cost of 4 necklaces = 4 x (1 u + 26) = 4 u + 104
Total cost of 7 rings and 4 necklaces
= 7 u + 4 u + 104
= 11 u + 104
11 u + 104 = 412
11 u = 412 - 104
11 u = 308
1 u = 308 ÷ 11 = 28
Cost of 10 necklaces = 10(1 u + 26) = 10 u + 260
Cost of 3 rings = 3 u
Amount that Olivia had at first
= 10 u + 260 + 3 u
= 13 u + 260
= 13 x 28 + 260
= $624
Answer(s): $624
