Algebra III/Trigonometry NotesName: ______

1.2 Setting up Equations-ApplicationsDate:______

Day 1 - Applied Word Problems

  1. Translate the following phrases into algebraic expressions:

a)5 times as large as xb) one-third of a cubed number xc) a number that exceeds x by 4

  1. Kinetic energy is one-half the product of the mass times the square of the velocity.
  1. Rachel is paid time-and-a-half for hours worked in excess of 36 hours. This week she earned $472.50 for working 42 hours. What is her normal hourly rate?
  1. Nick grossed $435 one week by working 50 hours. His employer pays time and a half for all hours worked over 40 hours. With this information, determine his regular hourly wage.
  1. Going into the final, which will count as 2/3 of the final grade, Sydney has test scores 86, 80, 84, and 90. What will Sydney need to score on her final in order to earn a B, which requires an average score of 80? What would be the lowest she could get to earn an A, or an average of 90?
  1. A car dealer, at a year-end clearance, reduces the list price of last year’s models by 15%. If a certain four door model has a discounted price of $18000, what is its list price? How much can be saved by purchasing last year’s model?

Day 2 – Investments and Interest

Investments

  1. A total of $18,000 is invested, some in stocks and some in bonds. If the amount invested in bonds is a third of that invested in stocks how much is invested in each category.
  1. A total of $18,000 is invested in bonds and certificates of deposit (CDs). If the amount invested in bonds exceeds the amount in CDs by $2,000, how much will be invested in each type.

Interest

Interest = (Principal)(rate)(time)

  1. If you are looking to earn $120 this year from a savings account that offers 2.5%, how much would you have to invest?
  1. Jared is retiring from being a neurosurgeon. He believes he will need $8,000 per year in extra income. He has $85,000 to invest and can invest in bonds paying 15% per year or in CDs paying 6% per year. How much money should be invested in each to realize exactly $8,000 in interest?
  1. A bank loaned out $16,000, part of it at a rate of 7% per year and the rest at a rate of 12% per year. If the interest received totaled $1000, how much was loaned out at 7%?
  1. Mr. Bontempo had $70,000 to invest. He invested part of the money into a 13% CD for 3 years and the rest into a 7% money market account for 2 years. How much must he invest into each account if he wants to earn a total of $25,000 in interest?