Question

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?

Answer 1

4 packs of medium cups and 6 packs of large cups

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 2

Ivy bought 4 packs of medium cups, and 6 packs of large cups.

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
`m` equal medium cups.

Let
`l` equal large cups.

`m+l=10`

`1.80m+2.40l=21.60`

Let's use substitution to solve this system.

Subtract
`l` from both sides of the first equation:

`m=10-l`

Let's substitute
`10-l` into the second equation for
`m`:

`1.80(10-l)+2.40l=21.60`

Distribute
`1.80` into
`(10-l)`:

`18-1.80l+2.40l=21.60`

Combine like terms:

`18+0.6l=21.60`

Subtract
`18` from both sides of the equation:

`-0.6l=3.60`

Divide by the coefficient of
`l`, which is
`0.6`:

`l=6`

Ivy bought 6 packs of large cups.

_

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

`m+6=10`

Subtract
`6` from both sides of the equation:

`m=4`

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`

`10=10`

2nd Equation Check:

`1.80(4)+2.40(6)=21.60`

`7.2+14.4=21.60`

`21.60=21.60`

Our answers are correct!