Question

If 3 boys can build 4 snowmen in 24 minutes how many will 9 boys finish building in an hour

Answer 1

Answer:

30 snowmen

Step-by-step explanation:

This is an example of a proportion, but in this case it involves 3 variables.

All we need to do is to take one as fixed variable and relate it with the other to know whether it is directly proportional or inversely proportional.

Let x be the number of snowmen 9 boys will finish building in an hour

But we first need to change 1 hour into minutes, thus; 1 hour=60 minutes

No. of boys            No. of snowmen           Time

     3 boys                       4 snowmen           24 min

     9 boys                             x                       60 min

We are going to take the number of snowmen as the fixed variable

{That is; $\frac{4}{x}$ = }  now , lets compare the number of snowmen to time, is it a direct proportion or indirect proportion? the more the time, the more the number of snowmen that will be build, this means, it is a direct proportion, so;

$\frac{4}{x}$ = $\frac{24}{60}$

Next is to compare the number of snowmen and the number of boys, the more the number of boys, the more the number of the snowmen that will be  build, this implies that it is a direct proportion, thus;

$\frac{4}{x}$ = $\frac{24}{60}$ × $\frac{3}{9}$

We can now proceed to simplify

$\frac{4}{x}$ = $\frac{24}{60}$ × $\frac{3}{9}$

$\frac{4}{x}$ = $\frac{72}{540}$

Cross -multiply

72× x  =  540× 4

72 x  =  2160

Divide both-side of the equation by 72

$\frac{72x}{72}$  =  $\frac{2160}{72}$

x   = 30  snowmen

Answer 2

Answer:

The boys can build 30 snowmen in an hour

Step-by-step explanation:

  Extracting the key information from the question:-

*** 3 boys can build 4 snowmen I 24 minutes.

*** 9 boys are to build  snowmen.

*** How many snowmen can be built by the 9 boys in an hour.

  Firstly, since 3 boys can build four (4) snowmen in 24 minutes, we need to convert one hour to minutes.

   60 minutes = 1 hour.

   Now, since three boys can build four (4) snowmen in twenty four (24) minutes, we need to know or find out how many snowmen  that none boys can build in the same time if they all work at the same rate as the three boys.

     

3 boys ------------- 4 snowmen (24minutes)

9 boys -------------- ? snowmen (24 minutes)

= 9/3  × 4

= 36/3

= 12 snowmen (24 minutes).

Now, 9 boys can build 12 snowmen in 24 minutes. All we now need to do is to determine or figure out  how many snowmen that the nine boys can build within an hour of work (60 minutes).

  Since nine boys can build 12 snowmen in 24 minutes, the number of snowmen that they can build in an hour (60 minutes) is:

(9 boys) 24 mins ------- 12 snowmen

(9boys) 60 mins --------- ? snowmen

  = 60/24  ×  12

 = 720/24

 = 30 snowmen

 Therefore, 9 boys can build 30 snowmen in one hour if they all build at the same rate as the initial three boys.