A maple syrup producer would like to increase production by 500 gallons per year with a goal of producing at least 20,000 gallons of syrup over the first period of production.
If the fist years's production, in gallons is given by x, write expressions for each of the other yearss' produtions.
year1=x year2= year3= year4= year5=
Find all possible values of syrup that could be produced in the first year to meet the goal of at least 20,000 gallons total over the five - year period.
Hahahej
3000
To find the expressions for the production in each of the other years, we need to consider that the maple syrup producer wants to increase production by 500 gallons per year.
Let's start with year 1. Given that year 1's production is represented by x gallons, year 2's production would be x + 500 gallons (increased by 500 gallons). Similarly, year 3's production would be (x + 500) + 500 = x + 1000 gallons.
Following this pattern, we can express the productions for years 1, 2, 3, 4, and 5 as follows:
year 1: x gallons
year 2: x + 500 gallons
year 3: (x + 500) + 500 = x + 1000 gallons
year 4: (x + 1000) + 500 = x + 1500 gallons
year 5: (x + 1500) + 500 = x + 2000 gallons
Now, let's find the possible values of syrup that could be produced in the first year to meet the goal of at least 20,000 gallons over the five-year period.
To achieve a total production of at least 20,000 gallons, we add the productions for all five years and set it equal to or greater than 20,000 gallons:
x + (x + 500) + (x + 1000) + (x + 1500) + (x + 2000) ≥ 20,000
Now, simplifying the equation:
5x + 5000 ≥ 20,000
Subtracting 5000 from both sides of the inequality:
5x ≥ 15,000
Dividing both sides of the inequality by 5:
x ≥ 3000
Therefore, the possible values of syrup that could be produced in the first year to meet the goal of at least 20,000 gallons over the five-year period are x ≥ 3000 gallons.