We will start with analyzing the background information into two groups, spending and revenue. (+) = revenue, (-) = spending.
(-) investment-$200
(-) cost to make lemonade-$2.00 a gallon
(-) cost to make cookies-$3.25 a dozen
(-) cost of business-$205.25
(+) sale price of lemonade- $0.50 a cup
(+) sale price of cookies-$0.75 a cookie
Following does not form part of the budget.
money hoping to earn from sales-$400
Part (c) Need an equality to show the condition to earn 3 times total spent.
We see that the amount spent / earned varies with the number of items sold, namely
L=number of cups of lemonades sold,
C=number of cookies sold.
Also note that one gallon = 16 cups (US measure) =>
cost of one cup of lemonade = $2/16 = $0.125
cost of one cookie = $3.25/12
In addition, we assume "investment" is necessary to run the business.
Money spent:
S=investment+0.125L+(3.25/12)C+cost of business
=200+0.125L+(3.25/12)C+205.25
=405.25+0.125L+(3.25/12)C
Money earned (revenue)
R=0.50L+0.75C
To satisfy required condistion, we need
R ≥ 3S
Expanded,
0.50L+0.75C ≥ 3(405.25+0.125L+(3.25/12)C)
0.50L+0.75C ≥ 1215.75+0.375L+(3.25/4)C)
Multiply both sides by 16
8L+12C - 6L - 13C ≥ 19452
and simplify
2L-C ≥ 19452
The inequality required is 2L-C ≥ 19452
