During a sale, 4 necklaces and 9 rings cost $595. If Emma bought 11 necklaces and 13 rings, she would have spent all her money. Each necklace cost $61 more than a ring. Find the amount that Emma had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
4 |
9 |
11 |
13 |
| Value |
1 u + 61 |
1 u |
1 u + 61 |
1 u |
| Total value |
4 u + 244 |
9 u |
11 u + 671 |
13 u |
Cost of 1 ring = 1 u
Cost of 9 rings = 9 u
Cost of 1 necklace = 1 u + 61
Cost of 4 necklaces = 4 x (1 u + 61) = 4 u + 244
Total cost of 9 rings and 4 necklaces
= 9 u + 4 u + 244
= 13 u + 244
13 u + 244 = 595
13 u = 595 - 244
13 u = 351
1 u = 351 ÷ 13 = 27
Cost of 11 necklaces = 11(1 u + 61) = 11 u + 671
Cost of 13 rings = 13 u
Amount that Emma had at first
= 11 u + 671 + 13 u
= 24 u + 671
= 24 x 27 + 671
= $1319
Answer(s): $1319
