Question

While Flinn was starting the fire, his friends were collecting firewood. Flinn has 5 sticks. If he puts 3 sticks in the fire every minute, and his friends bring 7 sticks every minute, how many minutes will they need to make a pile of 45 sticks next to their fire?

Answer 1

The time required to make a piles of 45 sticks is $\boxed{{\mathbf{10 minutes}}}$ .

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,

$\begin{aligned}{\text{in first minute}}&=5-3+7\\&=9\\\end{aligned}$

Now calculate the number of sticks in second minute as,

$\begin{aligned}{\text{in second minute}}&=9-3+7\\&=13\\\end{alined}$

Now calculate the number of sticks in third minute as,

$\begin{aligned}{\text{in third minute}}&=13-3+7\\&=17\\\end{aligned}$

Now calculate the number of sticks in fourth minute as,

$\begin{aligned}{\text{in fourth minute}}&=17-3+7\\&=21\\\end{aligned}$

Now calculate the number of sticks in fifth minute as,

$\begin{aligned}{\text{in fifth minute}}&=21-3+7\\&=25\\\end{aligned}$

Now calculate the number of sticks in sixth minute as,

$\begin{aligned}{\text{in sixth minute}}&=25-3+7\\&=29\\\end{aligned}$

Now calculate the number of sticks in seventh minute as,

$\begin{aligned}{\text{in seventh minute}}&=29-3+7\\&=33\\\end{aligned}$

Now calculate the number of sticks in eighth minute as,

$\begin{aligned}{\text{in eigth minute}}&=33-3+7\\&=37\\\end{aligned}$

Now calculate the number of sticks in ninth minute as,

$\begin{aligned}{\text{in ninth minute}}&=37-3+7\\&=41\\\end{aligned}$

Now calculate the number of sticks in tenth minute as,

$\begin{aligned}{\text{in tenth minute}}&=41-3+7\\&=45\\\end{aligned}$

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.

Answer 2

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 .............

$n^{th}$ 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