Ch. 2.7 notes Page 1 of 5
Ch2.7 Further Applications of Liner equations.
→ Mixture problems: 𝑏𝑎𝑠𝑒 × 𝑟𝑎𝑡𝑒(%) = 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 p=br
→ Interest problems: 𝐼(𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡) = 𝑃(𝑝𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙) × 𝑅(𝑟𝑎𝑡𝑒) × 𝑇(𝑡𝑖𝑚𝑒)
I=prt
→ Distance problems: 𝑟𝑎𝑡𝑒 × 𝑡𝑖𝑚𝑒 = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 d=rt
Ex1) a) If a chemist has 40L of a 35%acid solution, then the amount of pure acid in the solution
is?
b) If $1,300 is invested for one year at 7% simple interest, the amount of interest earned in
the year is?
c) Find the annual interest if $5,000 is invested at 4%.
Ch. 2.7 notes Page 2 of 5
Ex2) a) A chemist needs to mix 20L of a 40% acid solution with some 70% acid solution to
obtain a mixture that is 50% acid. How many liters of the 70% acid solution should be used?
b) A certain metal is 40% copper. How many kilograms of this metal must be mixed with 80kg of
a metal that is 70% copper to get a metal that is 50% copper?
Ch. 2.7 notes Page 3 of 5
Ex3) a) Elizabeth plans to invest part of it at 6% and $2,000 more than this amount at 7%. To
earn $790 per year in interest, how much should she invest at each rate?
b) Anna invested part of the money in a certificate of deposit at 4% and $3,000 more than that
amount in a bond paying 6%. Her annual interest income was $780. How much did Anna invest at
each rate?
Ch. 2.7 notes Page 4 of 5
Ex4) a) A bank teller has 25 more $5 bills than $10 bills. The total value of the money is $200.
How many of each denomination of bill does she have?
b) A man has $2.55 in quarters and nickels. He has 9 more nickels than quarters. How many
nickels and how many quarters does he have?
Ex5) a) If a men ran 100m for 9.77sec, what was his speed in meters per second?
Ch. 2.7 notes Page 5 of 5
b) If 66.64sec in the women’s 100m swimming event, what is the rate?
Ex6) Two cars leave Baton Rouge, Louisiana, at same time and travel east on interstate 10. One
travels at a constant speed of 55mph, and the other travels at a constant speed of 63mph. in
how many hours will distance between them be 24mi?
Ex7) Two planes leave Memphis at the same time. One heads south to New Orleans, the other
heads north to Chicago. The Chicago plane flies 50mph faster than the New Orleans plane. In
½hr, the planes are 275mi apart. What are their speeds?