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

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 2

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 $m$ 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!