ivy bought 10 packs of cups for her holiday party. a pack of medium cups costs $1.80 and a pack of large cups costs $2.40. she paid a total of $21.60. how many packs of each size cup did she buy?

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.

Let's use substitution to solve this system.

Subtract from both sides of the first equation:

Let's substitute into the second equation for :

Distribute into :

Combine like terms:

Subtract from both sides of the equation:

Divide by the coefficient of , which is :

Ivy bought 6 packs of large cups.

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Let's substitute into the first equation to find the number of medium cup packs:

Subtract from both sides of the equation:

Ivy bought 4 packs of medium cups.

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We can check our work 2 ways; by substituting our solved values into the initial equations.

1st Equation Check:

2nd Equation Check:

Our answers are correct!