# Writing Algebraic Expressions to Solve Word Problems Algebra

Writing Algebraic Expressions to Solve Word Problems.

Algebra is used every day to solve everyday problems. • For example: • You have a job and you get paid $8. 25 an hour. • You want to figure out how much pay you will receive if you worked 16 hours.

• You can write in words, I get paid $8. 25 for every hour I work. • Algebraically, you would write: • $8. 25 h • which means 8. 25 TIMES the number of hours you worked.

You should always write the formula FIRST for every question • SO, you would write • $8. 25 h = pay • Then, substitute the number of hours into the formula. • $8. 25(16) = p (pay) • Calculate the result • Your pay would be $132. 00 • Write your answer as p = $132. 00

Now it’s your turn. • Using the formula, calculate your pay if you worked: • 20 hours? • 32 hours? • 18. 5 hours? • 22 hours? • 110 hours? Every question must start with the formula $8. 25 h = p Then substitute into the formula the hours that you worked. Remember the answer is MONEY and should be in that form!

Now the same question with a twist! • If you got paid $189. 75, how many hours did you work? • You get paid $8. 25 an hour. • You can divide the pay by your rate of pay, ($8. 25) to get the number of hours you worked. Calculate and you find: • Algebraically, it would You worked, 23 hours! look like this.

New Problems • • • Some problems require that you know basic facts. How many seconds in a minute? How many minutes in an hour? How many hours in a day? How many days in a week? How many days in a year? How many weeks in a year? How many months in a year? How many centimetres in a meter? How many metres in a kilometer?

How Many Days in Three Weeks? • Since you know that there are 7 days in a week, you can write: • 7 days X the number of weeks = the number of days in a week. • Or Algebraically: • 7(w) = d • Substitute into the formula what you know. • 7(3)= d Calculate d = 21 • There are 21 days in three weeks!

How many hours in four days? • • • There are 24 hours in one day. So 24 d = hours in day 24 (4) = h h = 96 There are 96 hours in 4 days.

Using the facts, write a formula for each and solve. • • • How many days in 3 weeks? How many hours in 4 days? How many cm in 1500 meters? How many months in 13 years? How many weeks in 7 years? How many years in 3250 weeks? How many years in 250 months? How many minutes in 4 hours? How many hours in 17 days? How many kilometres in 4509 meters?

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