Ch. 2.7 notes Page 4 of 5
Ch2.7 Further Applications of Liner equations.
→ Mixture problems: base×rate%=percentage p=br
→ Interest problems: Iinterest=Pprincipal×Rrate×Ttime 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%.
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?
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?
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?
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?