Word problem to system of equations?

Question

a factory that makes backpacks can make 360 in a day. It takes 30 minutes to make a one strap, and 45 minutes to make a two strap backpack. The machine can only be on for 16 hours. X stands for two strap backpack, y stands for one strap. What is the system of equations for this problem?

Answer 1

Skyler, let's think about what the problem is telling us.

 

We have that 360 backpacks can be made in a day, both one and two-strap, so our first equation is x + y = 360

 

The second equation is going to be a bit tougher.  3 two strap backpacks would take 90 minutes, right?  30(3) = 90.  To make y one strap backpacks, it would take 30y minutes.  Using the same logic, it would take 45x minutes to make x two strap backpacks.

 

You would think this gives us 45x + 30y = 16, but there is one thing wrong here!

 

The 45 and 30 are minutes, and the 16 is hours.  We need to convert the minutes into hours or the hours into minutes.

 

We could either say (3/4)x + (1/2)y = 16, since 45 minutes is 3/4 of an hour and 30 minutes is 1/2 of an hour, orrrr,

 

we say 45x + 30y = 960, since 16 hours is 960 minutes.

 

Hope this helps!