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:

• $8.25h

• 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 • $8.25h = 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

$8.25h = 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.

• Algebraically, it would look like this.

h25.8$

75.189$

Calculate and you find:You worked, 23 hours!

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 metre?• How many metres in a kilometre?

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

• 24d = hours in day

• 24 (4) = h

• h = 96

• There are 96 hours in 4 days.

Homework

You KNEW it was coming!

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 metres?• How many months in 13 years?• How many weeks in 7 years?• How many years in 3250 weeks? (careful)• How many years in 250 months? (careful)• How many minutes in 4 hours? • How many hours in 17 days?• How many kilometres in 4509 metres? (careful)

This Slide Show can be found at February Homework on our Math

Web Site at:

https://hamptongrade8math.wikispaces.com/