Answer:
6 hours
Step-by-step explanation:
First, since they all collected 510, you divide 510 by 5, to figure out how much each person got.
You then know that each of them got 102 candies, so now, you subtract 12 from from 102, since the teacher gave them that much in the beginning.
You're left with 90, so last step is to divide 90 by 15, since they collect 15 every hour, which you get left with 6. Meaning they collected candies for 6 hours
Step-by-step explanation:
Sn= a+[n-1]d
S2= a+[2-1]d
8.5 = a+d _______Equation 1
S5 = a+[5-1]d
13=a+4d ________Equation 2
Subtract Equation 1 from Equation 2
13=a+4d
-
8.5= a+d
________
4.5= 3d
d=1.5
Substituting d=1.5 in equation 1
8.5=a+1.5
a=8.5-1.5
a=7
Sum of terms of an A.P =
Sn= n/2[2a+(n-1)d]
292= n/2[2×7+(n-1)d]
292=n/2[14+(n-1)1.5
292×2=n[14+(n-1)1.5]
584=n[14+1.5n-1.5]
584= 14n+1.5n²-1.5n
584= 1.5n²+12.5n
1.5n²+12.5n-584
1.5n²-24n+36.5n-584
1.5n(n-16)+36.5(n-16)
(1.5n+36.5)(n-16)
**n-16=0
n=16
To solve these type of problems is to simply invert the number after the division sign and multiply