I've been trying to prepare for the next ACT test but i just cant figure out how to do this one math problem, could you plz help me?
On his first day as a telemarkerter, Marshall made 24 calls. His goal was to make 5 more call on each succesive day than he made the day before. If Marshall met, but did not exceed, his goal, how many calls had he made in all after spending exactly 20 days making calls as a telemarketer?
a. 670
b. 690
c. 974
d. 1430
e. 1530
Thank you so much for your help!!!
2006-09-24 15:05:43 · 4 answers · asked by Sir Excalibur 2 in Science & Mathematics ➔ Mathematics
Ok so im seeing different answers....any one else agree with 1430 or 974?
2006-09-24 15:20:56 · update #1
The first day Marshall makes 24 calls, the next day 29, the next day 34, etc etc
24 + 5*(day - 1)
On the last day, he makes 24 + 5*(20-1) = 119
So on average, he makes 119 + 24 / 2 or 71.5 calls per day.
Over 20 days, 20 * 71.5 = 1430 calls
2006-09-24 15:15:58 · answer #1 · answered by Jeff S 2 · 0⤊ 0⤋
If you denote by a_i the number of calls in i-th day, you have the following:
a_1 = 24
a_2 = a_1 + 5 = a_1 + 1*5
a_3 = a_2 + 5 = a_1 + 5 + 5 = a_1 + 2*5
a_4 = a_3 + 5 = a_1 + 5 + 5 + 5 = a_1 + 3*5
......
a_20 = a_19 + 5 = a_1 + 5+....+5 = 19*5
Now you want to calculate the sum: a_1+a_2+...+a_20.
Summing up everyting you get:
20*a_1 + (0+1+2+...+19)*5 = 20*24 + 190*5 = 1430.
2006-09-25 00:12:55 · answer #2 · answered by Kris 1 · 0⤊ 0⤋
24 +5*19 + 5*18 + 5*17... 5*1 = 974
2006-09-24 22:13:16 · answer #3 · answered by Lo 2 · 0⤊ 1⤋
d. 1430
2006-09-24 22:18:31 · answer #4 · answered by Demiurge42 7 · 0⤊ 1⤋