Answer:
4 packs of medium cups and 6 packs of large cups
Step-by-step explanation:
1.80x + 2.40y = 21.60
1.80(4) + 2.40(6) = 21.60
7.2 + 14.4 = 21.60
21.60 = 21.60
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 [tex]m[/tex] equal medium cups.
Let [tex]l[/tex] equal large cups.
[tex]m+l=10[/tex]
[tex]1.80m+2.40l=21.60[/tex]
Let's use substitution to solve this system.
Subtract [tex]l[/tex] from both sides of the first equation:
[tex]m=10-l[/tex]
Let's substitute [tex]10-l[/tex] into the second equation for [tex]m[/tex]:
[tex]1.80(10-l)+2.40l=21.60[/tex]
Distribute [tex]1.80[/tex] into [tex](10-l)[/tex]:
[tex]18-1.80l+2.40l=21.60[/tex]
Combine like terms:
[tex]18+0.6l=21.60[/tex]
Subtract [tex]18[/tex] from both sides of the equation:
[tex]-0.6l=3.60[/tex]
Divide by the coefficient of [tex]l[/tex], which is [tex]0.6[/tex]:
[tex]l=6[/tex]
Ivy bought 6 packs of large cups.
_
Let's substitute [tex]6[/tex] into the first equation to find the number of medium cup packs:
[tex]m+6=10[/tex]
Subtract [tex]6[/tex] from both sides of the equation:
[tex]m=4[/tex]
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:
[tex](4)+(6)=10[/tex]
[tex]10=10[/tex]
2nd Equation Check:
[tex]1.80(4)+2.40(6)=21.60[/tex]
[tex]7.2+14.4=21.60[/tex]
[tex]21.60=21.60[/tex]
Our answers are correct!
