A fabric store sells two types of ribbon. One customer buys 3 rolls of the satin ribbon and had a total of 120 yards of ribbon. Another customer buys 2 rolls of lace ribbon and 4 rolls of the satin ribbon and has a total of 160 yards of ribbon. How many yards are on one rolls and one roll of satin ribbon?

Let [tex]x[/tex] be the yards in the satin ribbon roll and [tex]y[/tex] the yards in the lace ribbon roll.

Since 3 rolls of the satin ribbon are 120 yards, [tex]3x=120[/tex]. We can solve the equation to get the yards in one satin ribbon roll like follows:
[tex]3x=120[/tex]
[tex]x= \frac{120}{3} [/tex]
[tex]x=40[/tex]

Now that we know the yards in one roll of satin ribbon, lets find the yards in the lace ribbon one:
Since  2 rolls of lace ribbon and 4 rolls of the satin ribbon are 160 yards, [tex]2x+4y=160[/tex]. But remember that we already know the value of [tex]x[/tex] is 40, so lets replace that in our equation and solve for [tex]y[/tex] to get the yards in one roll of lace ribbon:
[tex]2x+4y=160[/tex]
[tex]2(40)+4y=160[/tex]
[tex]80+4y=160[/tex]
[tex]4y=160-80[/tex]
[tex]4y=80[/tex]
[tex]y= \frac{80}{4} [/tex]
[tex]y=20[/tex]

We can conclude that there are 40 yards in the roll of satin ribbon, and 20 yards in the roll of lace ribbon.