Answer:
b) x ≥ 3000 gallons
Step-by-step explanation:
Part a)
Production of Year 1 = x gallons
By each year the producer will increase the production by 500 gallons. So,
Production in Year 2 = x + 500 gallons
Similarly,
Production in Year 3 = x + 500 + 500 = x + 1000 gallons
Production in Year 4 = x + 1000 + 500 = x + 1500 gallons
Production in Year 5 = x + 1500 + 500 = x + 2000 gallons
Part b)
The maple syrup producer wants to produced atleast 20,000 gallons in 5 years.
Total amount produced in 5 years = x + x + 500 + x + 1000 + x + 1500 + x + 2000
Total amount produced in 5 years = 5x + 5000
Since, producer wants total production to be atleast 20,000, we can set up the inequality as:
5x + 5000 ≥ 20000
Subtracting 5000 from both sides, we get:
5x ≥ 15000
Dividing both sides by 5, we get:
x ≥ 3000
This means, in the first year the production of maple syrup must be atleast 3,000 gallons i.e 3000 gallons or more to have a total of atleast 20,000 gallons in 5 years.
