Aunt Jessica said to her nephew Stan:

• "A neighbor of mine purchased a certain quantity of Beef at two shillings a pound, and the same quantity of Sausages at eighteen pence a pound."
• "Stan pointed to her that if she had divided the same money equally between Beefs and Sausages, she would have gained two pounds in total weight."

Determine exactly how much Aunt Jessica's neighbor did spend on the two items.

Note:
12 pence = 1 shilling
20 shillings = 1 Pound Stirling

****** Adapted from an original problem by H. E. Dudeney.

Beef price 24 pence per pound
Sausage price 18 pence per pound
x is weight of each puchase, 2x purchased in all
"Gained" means she would have bought 2 more pounds of weight than she actually bought.
At first I misunderstood the word "gained" and I thought it meant that her entire purchase would have weighed 2 pounds exactly, but that led to a fractional number of shillings.

Money spent = 24(pence/pound)*x(pounds) + 18(pence/pound)*x(pounds)  = 42x pence
Half the money = 21x pence

Hypothetical equal money case
Beef weight = 21x pence / 24(pence/pound) = (7/8)x pounds
Sausage weight = 21x pence / 18(pence/pound) = (7/6)x pounds
Actual weight bought: 2x
Gained weight hypothetically: 2
(2x + 2) pounds = ((7/8) + (7/6))*x = ((42+56)/48)x pounds = (49/24)x
2x + 2 = (49/24)x
2 = x/24
x = 48
Money spent = 42x = 42*48 = 6*48 = 2016 shillings

8 pounds Stirling, 8 Shillings
She actually bought 48 pounds (weight) each of beef and of sausage: 96 total
Hypothetically, she could have bought 42 pounds beef plus 56 pounds sausage: 98 total

Posted by Larry on 2023-08-15 08:52:53