Respuesta :
Answer:
Time required to make a pile of 45 sticks next to their fire = 10 minutes
Step-by-step explanation:
This is an example of arithmetic progression.
First term = 5 - 3 + 7 = 9 sticks
Common difference = 7 - 3 = 4 sticks.
So the number of sticks next to their fire is increasing like this
9, 13, 17, 21 .............
[tex]n^{th}[/tex] term of AP = a + (n-1) d, we need to find n
a + (n-1) d = 45
9 + (n-1) x 4 = 45
(n-1) x 4 = 36
n - 1 = 9
n = 10
Time required to make a pile of 45 sticks next to their fire = 10 minutes
The time required to make a piles of 45 sticks is [tex]\boxed{{\mathbf{10 minutes}}}[/tex] .
Further explanation:
Given:
It is given that Flinn is starting the fire. Initially Flinn has 5 sticks and every minute he puts 3 sticks in the fire and he get 7 sticks back from his friends every minute.
Step by step explanation:
Step 1:
Flinn has 5 sticks initially.
In every minute Flinn puts 3 sticks in the fire and he get 7 sticks back from his friends every minute.
In the next minute he puts 3 sticks in the fire and his friends brings 7 sticks every minute.
Now calculate the number of sticks in next first minute as,
[tex]\begin{aligned}{\text{in first minute}}&=5-3+7\\&=9\\\end{aligned}[/tex]
Now calculate the number of sticks in second minute as,
[tex]\begin{aligned}{\text{in second minute}}&=9-3+7\\&=13\\\end{alined}[/tex]
Now calculate the number of sticks in third minute as,
[tex]\begin{aligned}{\text{in third minute}}&=13-3+7\\&=17\\\end{aligned}[/tex]
Now calculate the number of sticks in fourth minute as,
[tex]\begin{aligned}{\text{in fourth minute}}&=17-3+7\\&=21\\\end{aligned}[/tex]
Now calculate the number of sticks in fifth minute as,
[tex]\begin{aligned}{\text{in fifth minute}}&=21-3+7\\&=25\\\end{aligned}[/tex]
Now calculate the number of sticks in sixth minute as,
[tex]\begin{aligned}{\text{in sixth minute}}&=25-3+7\\&=29\\\end{aligned}[/tex]
Now calculate the number of sticks in seventh minute as,
[tex]\begin{aligned}{\text{in seventh minute}}&=29-3+7\\&=33\\\end{aligned}[/tex]
Now calculate the number of sticks in eighth minute as,
[tex]\begin{aligned}{\text{in eigth minute}}&=33-3+7\\&=37\\\end{aligned}[/tex]
Now calculate the number of sticks in ninth minute as,
[tex]\begin{aligned}{\text{in ninth minute}}&=37-3+7\\&=41\\\end{aligned}[/tex]
Now calculate the number of sticks in tenth minute as,
[tex]\begin{aligned}{\text{in tenth minute}}&=41-3+7\\&=45\\\end{aligned}[/tex]
Now it can be seen that in tenth minute the number of fire sticks are 45.
Therefore, they will need 10 minutes to make a piles of 45 sticks.
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Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Addition and subtraction
Keywords: Flinn, fire, sticks, collection, firewood, subtraction, number, addition, friends, fire, pile, starting, minute.
