MATH SOLVE

3 months ago

Q:
# A maple syrup producer would like to increase production by 500 gallons per each consecutive year with a goal of producing at least 20,000 gallons of syrup cumulatively for the first five year period of production.If the first year’s production, in gallons, is given by x, write expressions for each of the other years’ productions.Year 1 = x Year 2 = Year 3 = Year 4 = Year 5 =b) Find all possible values of syrup that could be produced the first year to meet the goal of at least 20,000 gallons cumulatively over the five-year period. You must set up a mathematical formula/rule and solve algebraically.

Accepted Solution

A:

Answer:b) x ≥ 3000 gallonsStep-by-step explanation:Part a)Production of Year 1 = x gallonsBy each year the producer will increase the production by 500 gallons. So,Production in Year 2 = x + 500 gallonsSimilarly,Production in Year 3 = x + 500 + 500 = x + 1000 gallonsProduction in Year 4 = x + 1000 + 500 = x + 1500 gallonsProduction in Year 5 = x + 1500 + 500 = x + 2000 gallonsPart 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 + 5000Since, producer wants total production to be atleast 20,000, we can set up the inequality as:5x + 5000 ≥ 20000Subtracting 5000 from both sides, we get:5x ≥ 15000Dividing both sides by 5, we get:x ≥ 3000This 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.