Sammy and david were selling water bottles to raise money for new football uniforms. sammy sold 5 bottles for every 3 water bottles. david sold. together. they sold 160 water bottles. how many did each boy sell?

X=number of bottles sold by Sammy.
y=number of bottles sold by David.
We can suggest the following system of equations:

x/y=5/3
x+y=160

We solve the system of equations by substitution method.

x+y=160        ⇒y=160-x

x/(160-x)=5/3
3x=5(160-x)
3x=800-5x
3x+5x=800
8x=800
x=800/8
x=100

y=160-x
y=160-100
y=60

Sammy sold 100 bottles and David sold 60 bottles.

other method.
5x=bottles sold by Sammy
3x=bottles sold by David.

We can suggest the following equation:
5x+3x=160
8x=160
x=160/8
x=20

bottles sold by Sammy: 5x=5(20)=100
bottles sold by David:  3x=3(20)=60

Sammy sold 100 bottles and David sold 60 bottles.