During a sale, 11 necklaces and 12 rings cost $1797. If Tiffany bought 14 necklaces and 13 rings, she would have spent all her money. Each necklace cost $63 more than a ring. Find the amount that Tiffany had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
11 |
12 |
14 |
13 |
| Value |
1 u + 63 |
1 u |
1 u + 63 |
1 u |
| Total value |
11 u + 693 |
12 u |
14 u + 882 |
13 u |
Cost of 1 ring = 1 u
Cost of 12 rings = 12 u
Cost of 1 necklace = 1 u + 63
Cost of 11 necklaces = 11 x (1 u + 63) = 11 u + 693
Total cost of 12 rings and 11 necklaces
= 12 u + 11 u + 693
= 23 u + 693
23 u + 693 = 1797
23 u = 1797 - 693
23 u = 1104
1 u = 1104 ÷ 23 = 48
Cost of 14 necklaces = 14(1 u + 63) = 14 u + 882
Cost of 13 rings = 13 u
Amount that Tiffany had at first
= 14 u + 882 + 13 u
= 27 u + 882
= 27 x 48 + 882
= $2178
Answer(s): $2178
