Question: Tony wanted to buy a watch which costs $76. He saves $6 on the first day. Each succeeding day he saves $1 more than the previous day. If he continues this pattern of savings, in how many days can he buy the watch?
A ) 76 B ) 70 C ) 8 D ) 19
Steps to derive
1 The money Tony saves increases by $1 each day. So, daily savings form an arithmetic sequence: 6, 7, 8, 9, ..... [Analyse and understand the problem.]
2 $76 will be the sum to n terms of an arithmetic series.
3Sn = n[2a1+(n-1)d]2 [Formula for the sum of an arithmetic series.]
4 76 = n[2(6)+(n-1)1]2 [Replace Sn = 76, a1 = 6, d = 1.]
5 152 = n[12 + n -1] [Cross multiply.]
6 152 = n2 + 11n [Simplify.]
7n2 + 11n - 152 = 0
8n = 8, - 19 [Solve for n.]
9 So, Tony can save $76 in 8 days to buy the watch. [The number of days cannot be negative and so, n = - 19 is not possible.]
