Question

3. Carrie and Juanita are saving up to start a slime business. They need at least $125 to cover their start up costs. To earn that money, Carrie decides to do sell cupcakes. She sells cupcakes for $0.50 each. Juanita decides that she would like to sell homemade cards. She will be selling the cards for $2.25 each. Juanita plans to make at least 35 cards. To make up the difference, Carrie plans to sell no less than 3 times the number of cards Juanita makes.

Write a set of constraints to model the problem, with x representing the number of cards created and y representing the number of cupcakes.

Answer 1

Constraints:

`0.50y+2.25x\geq 125\\x\geq 35\\y\geq 3x`

Explanation:

Let x represents the number of cards and y represents the number of cupcakes.

Carrie decides to sell cupcakes for $0.50 each.

Total amount earned from selling cupcakes
`=0.50y`

Juanita decides to sell homemade cards for $2.25 each.

Total amount earned from selling cards
`=2.25x`

As Carrie and Juanita need at least $125 to cover their start up costs,

`0.50y+2.25x\geq 125`

Juanita plans to make at least 35 cards.

`x\geq 35`

Carrie plans to sell cupcakes no less than 3 times the number of cards Juanita makes.

`y\geq 3x`

Constraints:

`0.50y+2.25x\geq 125\\x\geq 35\\y\geq 3x`