College Algebra & Trigonometry, 2018a

80 CHAPTER 1. ALGEBRA REVIEW
Addendum - Word Problems
Following are a selection of word problems - some from ancient times, some from
the Renaissance and Enlightenment, and some from the 19th and 20th century.
1) A teacher agreed to work 9 months for $562.50 and board. At the end of
the term, on account of two months absence caused by illness, he received only
$409.50 for his seven months work. If the teacher used all nine months of his
board during the term, what was his board per month? (American 1892)
2) A servant is promised $100 plus a cloak as wages for a year. After seven
months, he leaves and receives $20 plus the cloak. How much is the cloak worth?
(Clavius, German 1608)
3) The sales tax on garments is 1 of their value. A certain man buys 42 garments,
paying in copper coins. Two garments and 10 copper coins are paid as
20
tax. What is the price of a garment, O learned one? (Ancient India)
4) Two wine merchants enter Paris, one of them with 64 casks of wine, the
other with 20 casks (all of the same value). Since they do not have enough money
to pay the customs duties, the first pays 5 casks of wine and 40 francs, and the
second pays 2 casks of wine and receives 40 francs change. What is the price of
each cask of wine and what is the duty on each cask? (Chuquet, French 1484)
5) One of two men had 12 fish and the other had 13 fish, and all of the fish
were of the same price. From the first man, a customs agent took away 1 fish and
12 denarii for payment. From the other man he took 2 fish and gave him back 7
denarii as change. Find the customs fee and the price of each fish.
(Fibonacci, Italian 1202)
6) Two traders transporting sheepskins approach their country’s border. The
first trader has 100 sheepskins and the border guard takes 10 sheepskins plus $25
as a tariff. The second trader has 42 sheepskins and for a tariff, the border guard
takes 7 sheepskins but returns $14 change. What is the tariff per sheepskin and
what is the value of each sheepskin?