Word Problem

Mogorosi wrote:Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 276 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 3 of the days were hot, then what was the price of 1 cup on a hot day?

A $1.50
B 1.88
C 2.25
D 2.50

IOM answer (A $1.50 deleted)

hot cup =1.875

solution follows

SP - CP = $276
SP = 7days normal + 3 days hot
= 7x + 3*(1.25)x
total cups sold each day = 32
Total Sp = 32 [7x + (15/4)x]
CP = 32*10*75 cents = 32*10*3/4 dollars.
32 [7x + (15/4)x] - 32*10*3/4 = 276
32*43/4(x) = 276 + 240
8*43*x = 516
x approx 1.5
5/4*1.5 = price for hot cup = 1.88

Total cost of lemonade sold = 32 (Sales per day) *10 (Days) * 0.75 (Unit cost) = 240

Profit = 276, Sales Revenue (Sales*Price) = Profit+Cost = 240 + 276 = 516

Set Equation:

516 (Sales Revenue) = [3 (P, regular price) *1.25 + 7 (P, regular price)] * 32 (Sales per day)
.....................in the parentheses 3P*1.25+7P ..... 3 and 7 are set to the number of days, which are 10

516=(10.75*P)*32;
P=1.5

Hot cup P*1.25 = 1.5*1.25 = 1.875

beat_gmat_09 wrote:SP - CP = $276
SP = 7days normal + 3 days hot
= 7x + 3*(1.25)x
total cups sold each day = 32
Total Sp = 32 [7x + (15/4)x]
CP = 32*10*75 cents = 32*10*3/4 dollars.
32 [7x + (15/4)x] - 32*10*3/4 = 276
32*43/4(x) = 276 + 240
8*43*x = 516
x approx 1.5
5/4*1.5 = price for hot cup = 1.88

i like your solution but please document it properly; what is x?

Mogorosi wrote:

beat_gmat_09 wrote:SP - CP = $276
SP = 7days normal + 3 days hot
= 7x + 3*(1.25)x
total cups sold each day = 32
Total Sp = 32 [7x + (15/4)x]
CP = 32*10*75 cents = 32*10*3/4 dollars.
32 [7x + (15/4)x] - 32*10*3/4 = 276
32*43/4(x) = 276 + 240
8*43*x = 516
x approx 1.5
5/4*1.5 = price for hot cup = 1.88

i like your solution but please document it properly; what is x?

SP = selling price for 32 cups on 7 days + 32 cups on 3 hot days.
CP = cost price of cups is 32*75 cents for 10 days = 32*75*10 cents, convert it to dollars = (32*75*3)/4 ........... (2)
SP - CP = Profit earned = $273

let x be the price of one cup on normal day, then price of 1 cup on hot day is 1.25x or (5/4)x

Total Selling price for 10 days; each day 32 cups are sold = 32 [7x + (15/4)x] .................... (1)

SP - CP = 276
i.e. (1) - (2) = 276
32 [7x + (15/4)x] - (32*75*3)/4 = 276
Solving for x gives x = 1.5 = price of 1 cup on normal day.
Price for 1 hot cup = 1.5*1.25 or 1.5*(5/4) = 1.88