Question

Cheryl Falkowski has a collection of silver spoons from all over the world. She finds that she can arrange her spoons in sets of 7 with 1 left​ over, sets of 8 with 7 left​ over, or sets of 15 with 3 left over. If Cheryl has fewer than 200​ spoons, how many are​ there?

Answer 1

Sets of 7 with 1 left over : 8,15,22,29,36,43,50,57,64,71,78,85,92,99,106,113,120,127,134,141,148,155,162,169,176,183,190,197

sets of 8 with 7 left over :
15,23,31,39,47,55,63,71,79,87,95,103,111,119,127,135,143,151,159,167,175,183,191,200

sets of 15 with 3 left over : since we have 183 in both the previous ones we did....lets try it...183/15 = 12 R 3

so ur answer is 183 spoons <== there is probably an easier way to do this, I just dont know it