I need help with this problem!

Question

Lilith makes soap and lotion. It takes her 20 minutes to make a batch of soap and 35 minutes to make a batch of lotion. The costs of producing each batch are 5 dollars for the soap and 15 dollars for the lotion. Lilith has 20 hours available to make soap and lotion. The materials to make the soap and lotion must cost at most 325 dollars. The system of inequalities represents this situation.

5x+15y<=325

20x+35y<=1200

What does the solution (53,4) represent? Please write in complete sentences and describe things clearly.

Answer 1

Hello,

I feel like I need more information to give the most accurate response.

This is my reasoning based on the information provided. Please comment if you need more understanding.

1st. The ordered pair (53,4) represents (Soap is X, Lotion is Y)

1. If I enter 5(53) + 15(4) less than or equal to 325 - this equation solves for the cost to produce.
2. It took $265 dollars to produce 53 batches of soap and $60 to produce 4 batches of lotion. She stayed within her budget.
3. 2nd. 20(53) + 35(4) less than or equal to 1200 min which is the same as 20 hours (1200/60 = 20)
4. It took Lilith 1060 min or 17.66 hours to make 53 batches of soap and 140 min or 2.33 hours to make 4 batches of lotion she staid within her time limit

Answer 2

53 is the amount of soap and 4 the amount of lotion she makes for $325

5(53) + 15(4)= 265 + 60 = 325,$5 for 53 soaps + $15 per 4 lotions.

and 53 is the amount of soap and 4 the amount of lotion that she can make within 20x60= 1200 minutes

20(53) + 35(4) = 1060 + 140 = 1200 minutes

20 minutes for 53 soap + 35 minutes for 4 lotion each = 1200 minutes= 20 hours max