# Systems of Equations real life scenario: m+s=12, 6m+4s=?

#### falcios

##### New member
Each month for a year, purchase amounts will vary. It can be either $4 or$6

How can I set up a systems of equations to figure out the 2nd equation's minimum dollar value?

m+s=12

6m+4s=?

#### lev888

##### Junior Member
Each month for a year, purchase amounts will vary. It can be either $4 or$6

How can I set up a systems of equations to figure out the 2nd equation's minimum dollar value?

m+s=12

6m+4s=?

Why minimum? You don't have the actual value?

#### falcios

##### New member
Why minimum? You don't have the actual value?
Do you have a real life scenario or not? Do you have the total amount and want to find m and s? Let's say you paid for a service monthly, either $4 or$6 and the total was $60. Now you want to figure out how many times you paid$4 and how many times $6. In this case we get this system: m+s=12 6m+4s=60 If you do NOT have the total value, then I am not sure what you trying to do. #### falcios ##### New member Sorry for the confusion. It is a real life scenario. I figured out manually the$60 amount.

I wanted to know if it was possible to arrive at the $60 amount if I didn't know the number beforehand. Do you suggest another method to get the$60 answer?

#### lev888

##### Junior Member
Sorry for the confusion. It is a real life scenario. I figured out manually the $60 amount. I wanted to know if it was possible to arrive at the$60 amount if I didn't know the number beforehand.

Do you suggest another method to get the $60 answer? Could you share the scenario? I still don't understand what you trying to do. Is it close to my example above? Where does$60 come from?

If you don't know the total it's not possible to calculate it - there are multiple solutions. E.g. you paid $4 12 times, the total is$48. You paid $6 12 times, the total is$72. And all the combinations in between. If you want the least possible value for the total it would be \$48.