Answer:
60
Step-by-step explanation:
Since both bags of sugar were 120 kg, there is a total of 240 kg of sugar to be distributed into the packs. Let x represent the number of 2 kg packets and y represent the number of 3 kg packets. We know that all the sugar was packed into these two kinds of packets, so:
[tex]2x+3y=240[/tex]
And we know that there were half as many 2 kg packets as 3 kg packets, so:
[tex]x=\frac{1}{2} y[/tex]
Now, we have a system of equations!
[tex]\left \{ {{2x+3y=240} \atop {x=\frac{1}{2}y }} \right.[/tex]
Let's put the second equation equal to y, since that removes the fraction:
[tex]x=\frac{1}{2}y\\ 2x=y[/tex]
Now substitute y into the first equation:
[tex]2x+3y=240\\2x+3(2x)=240[/tex]
Now simplify to find x:
[tex]2x+3(2x)=240\\2x+6x=240\\8x=240\\x=30\\[/tex]
There are 30 of the 2 kg packets! Now, we can use x to find y, the number of 3 kg packets!
[tex]2x=y\\2(30)=y\\60=y[/tex]
There are 60 of the 3 kg packets!
