Solving Word Problems“When will I ever use this stuff?”

Discounts

Percentage problems are solved using proportions.› (100 - %) New

100 =

Old

› If you have a coupon that gives you a 15% discount on your groceries and your total bill was $155, what would it have cost you without the coupon?

Set up the proportion to get the answer.

85x = 15500

x = $182.35

Mark-ups

Mark-ups are the idea that stores charge more than they paid for a product in order to make a profit.

Use the same proportion as before except you add:› (100 + %) New

100 =

Old

WHY???

Mark-ups

A bookstore buys a book from the publisher for $71 and the store policy is to mark up all books 32% before putting them on the shelves for customers to purchase. How much should the bookstore charge for the book?

100x = 9372

x = 93.72

The bookstore should charge $93.72 for the book.

Puzzles Define your variable.

Set up the equation.A typical college student spends 1/3 of her waking time in class, 1/4 of her waking time eating, 1/12 of her waking time working out, 3 hours studying, and 2.5 hours doing other things. How many hours of sleep does the typical college student get?

Solve for the variable.

Answer the question asked!!

Let x = total time awake

()12

4x + 3x + x + 66 = 12x

8x + 66 = 12x

66 = 4x

x = 16.5

7.5 hours of sleep

Money, Money, Money….

Interest is money paid for the use of money.

Banks pay interest to you if you have a savings account of some kind because they are “using” your money.

You pay the bank interest when you borrow money from them to buy things.

Interest charges can get you in trouble!! If you get a credit card, always pay the total amount to avoid these charges!

Money, Money, Money… Simple Interest –

› I = Prt I is the interest charged (or earned) P is the principal invested (or borrowed) r is the interest rate expressed as a decimal t is the time the money is invested in years

If you invest $1400 in a CD for 5 years at a rate of 3%, how much interest do you earn?› P = 1400 r = .03 t = 5› I = (1400)(.03)(5)› I = $210

So, after 5 years you would have $1610!!!

Money, Money, Money….. Sometimes, people split their money into different

accounts to maximize their earning potential and minimize their risk.› Michael has $10,000 to invest. He put some of it in a CD that

earns 2% per year and the rest in a money market account that earns 12% per year. If he earned $750 in interest after the first year, how much did he invest in each account?

› Let x = the amount invested in the CD. (x)(.02)(1) The interest earned on the CD. (10000-x)(.12)(1) The interest earned on the money

market account. .02x + 1200 - .12x = 750 1200 - .1x = 750 -.1x = -450 x = 4500

So, Michael invested $4500 in the CD and $5500 in the money market account.