During a sale, 5 necklaces and 10 rings cost $1260. If Hilda bought 7 necklaces and 9 rings, she would have spent all her money. Each necklace cost $12 more than a ring. Find the amount that Hilda had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
5 |
10 |
7 |
9 |
| Value |
1 u + 12 |
1 u |
1 u + 12 |
1 u |
| Total value |
5 u + 60 |
10 u |
7 u + 84 |
9 u |
Cost of 1 ring = 1 u
Cost of 10 rings = 10 u
Cost of 1 necklace = 1 u + 12
Cost of 5 necklaces = 5 x (1 u + 12) = 5 u + 60
Total cost of 10 rings and 5 necklaces
= 10 u + 5 u + 60
= 15 u + 60
15 u + 60 = 1260
15 u = 1260 - 60
15 u = 1200
1 u = 1200 ÷ 15 = 80
Cost of 7 necklaces = 7(1 u + 12) = 7 u + 84
Cost of 9 rings = 9 u
Amount that Hilda had at first
= 7 u + 84 + 9 u
= 16 u + 84
= 16 x 80 + 84
= $1364
Answer(s): $1364
