A customer at a store paid $42 for 4 pairs of pants and 3 shirts. At the same store, a second customer paid $2 more for 1 pair of pants and 7 shirts. The price of each pair of pants is the same, and the price of each shirt is the same. Which system of equations can be used to find the price in dollars of each pair of pants, x, and each shirt, y?

The system of Equations:

4x + 3y = 42

x + 7y = 44

Step-by-step explanation:

Let the price in dollars of

each pair of pants = x

each shirt = y

A customer at a store paid $42 for 4 pairs of pants and 3 shirts.

Hence:

4 × x + 3 × y = $42

4x + 3y = 42

At the same store, a second customer paid $2 more for 1 pair of pants and 7 shirts.

This means he, paid $42 +$2 = $44

Hence:

1 × x + 7 × y = 44

x + 7y = 44

The system of equations can be used to find the price in dollars of each pair of pants, x, and each shirt, y is

4x + 3y = 42 Equation 1

x + 7y = 44 Equation 2

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!