Answer:
Ivy bought 4 packs of medium cups, and 6 packs of large cups.
Step-by-step explanation:
To solve this problem, we will have to use a system of equations. Our first equation will represent the cups, and our second equation the costs.
Let
equal medium cups.
Let
equal large cups.
![m+l=10](https://tex.z-dn.net/?f=m%2Bl%3D10)
![1.80m+2.40l=21.60](https://tex.z-dn.net/?f=1.80m%2B2.40l%3D21.60)
Let's use substitution to solve this system.
Subtract
from both sides of the first equation:
![m=10-l](https://tex.z-dn.net/?f=m%3D10-l)
Let's substitute
into the second equation for
:
![1.80(10-l)+2.40l=21.60](https://tex.z-dn.net/?f=1.80%2810-l%29%2B2.40l%3D21.60)
Distribute
into
:
![18-1.80l+2.40l=21.60](https://tex.z-dn.net/?f=18-1.80l%2B2.40l%3D21.60)
Combine like terms:
![18+0.6l=21.60](https://tex.z-dn.net/?f=18%2B0.6l%3D21.60)
Subtract
from both sides of the equation:
![-0.6l=3.60](https://tex.z-dn.net/?f=-0.6l%3D3.60)
Divide by the coefficient of
, which is
:
![l=6](https://tex.z-dn.net/?f=l%3D6)
Ivy bought 6 packs of large cups.
_
Let's substitute
into the first equation to find the number of medium cup packs:
![m+6=10](https://tex.z-dn.net/?f=m%2B6%3D10)
Subtract
from both sides of the equation:
![m=4](https://tex.z-dn.net/?f=m%3D4)
Ivy bought 4 packs of medium cups.
_
We can check our work 2 ways; by substituting our solved values into the initial equations.
1st Equation Check:
![(4)+(6)=10](https://tex.z-dn.net/?f=%284%29%2B%286%29%3D10)
2nd Equation Check:
![1.80(4)+2.40(6)=21.60](https://tex.z-dn.net/?f=1.80%284%29%2B2.40%286%29%3D21.60)
![7.2+14.4=21.60](https://tex.z-dn.net/?f=7.2%2B14.4%3D21.60)
![21.60=21.60](https://tex.z-dn.net/?f=21.60%3D21.60)
Our answers are correct!