A woodworking artist makes two types of carvings: type X and type Y. He spends 3 hours making each type X carving and 2 hours making each type Y carving, and he can spend up to 36 hours each week making carvings. His materials cost him $4 for each type X carving and $5 for each type Y carving. and he must keep his weekly cost for materials to $100 or less. If x is the number of type X carvings he makes in a week and y is the number of type Y carvings he makes in a week, which of the following systems of inequalities models this situation?

To find :  System of Inequalities denoting artists' type X & Type Y carvings.

Given : Carving X & Y require 3 & 2 hours respectively, total time = 36 hours per week.

Cost of carving X & Y = $4 & $5 respectively, total cost = upto 100

So, following are inequalities equations, for time & money required for both carvings :

Time Inequality Equation : 3x + 2y < 36

Money Inequality Equation : 4x + 5y <  100

Hence, System of Inequalities = 3x + 2y < 36 ; 4x + 5y <  100

To learn more , refer : link

Step-by-step explanation:

1 inequality will model the number of hours he spends on the carvings per week and the other inequality will model the amount of money he will spend on materials per week.

He spends 3 hours on type X and 2 hours on type Y, so

3X + 2Y models the hours he spends on each. If he can spend up to 36 hours per week, the inequality sign is less than or equal to. Therefore, the inequality for the number of hours he can spend per week on type X and Y carvings is

3X + 2Y ≤ 36

Now for the money inequality.

He spends $4 for type X carvings and $5 for type Y carvings, so 4X + 5Y models that part of the inequality. If he can spend up to $100 per week, the inequality sign is less than or equal to here as well.

4X + 5Y ≤ 100

Those are the 2 inequalities that make up the system.

step-by-step explanation: