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

Answer:

Constraints:

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

Step-by-step 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:

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