At a hockey game, a vender sold a combined total of 176 sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and the number of hot dogs sold.

Hot dogs sold: 44

Sodas sold: 132

Step-by-step explanation:

This is is a problem of a system of two equations with two unknowns. This can be solved in multiple ways (the substitution method, the elimination method, the equalization method, the graphic method...) . I will resolve it using the equalization method that is a little bit more practical from my point of view.

First, we have to determine the system by the data we are given:

Where:

Secondly, we are going to isolate any variable from both equations. I chose to isolate Y.

Thirdly, we equalizate both equations.

So we get:

Then we isolate X.

So now we know that the number of hot dogs sold was 44! If the sodas sold were three times the number of hot dogs sold, then we know that there were 132 sodas sold at the hockey game!

i belive those are the ones that are under 90 degreese.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!