Algebra ( Period 4)

CHAPTER 2-1: STRATEGIES FOR TRANSLATING

TO ALGEBRAIC EQUATIONS

The notes are below but you should already know this!

Try the homework and come with questions.

The only part of this section that will not be familiar:

TRANSLATING GIVEN INFORMATION INTO YOUR OWN WORD PROBLEM…YOU’RE WRITING A STORY!
I’ve included example 5 from your book below (p. 77)
Maxine’s time every time she drove = t
Tia’s time every time she drove = t + 4
Given: 2t + (t + 4) = 28
Write a word problem or story

Maxine and Tia took a trip together and took turns driving.
Maxine took 2 turns driving and Tia only 1, but when Tia drove, she drove 4 more hours than Maxine drove on each of her turns.
The trip took 28 hours.
How long did each of them drive?

Algebraic expressions just are the ones that have variables
Numeric expressions have only numbers
Equations must have an = sign while expressions do not

STRATEGY #1:TRANSLATE WORD BY WORD
You did this in Chapter 1!
Always try this first.
Just be careful of less THAN and subtracted FROM because these are switched from the order that you read/say them:
A number less THAN 12 is 12 – n but if you say a number less 12, this would be n – 12
12 subtracted FROM a number is n – 12, but 12 subtract a number would be 12 – n

The only other translation to be careful of is when you multiply a SUM or DIFFERENCE by a number or variable:
12 times the SUM of a number and 5 is 12(n + 5), but the sum of 12 times a number and 5 would  be 12n + 5
12 times the DIFFERENCE of a number and 5 is 12(n – 5), but the difference of 12 times a number and 5 would be 12n – 5

If you have 2 or more unknowns, use different variables:
The difference of a number and ANOTHER number would be x - y

STRATEGY #2: DRAWING A PICTURE
(When in doubt, draw it out! ;)
I have 5 times the number of quarters as I have dimes.
I translate to: 5Q = D
I check: If I assume that I have 20 quarters, then 5(20) = 100 dimes
Does this make sense? That would mean I have a lot more dimes than quarters.
The original problem says I have a lot more quarters!
My algebra is WRONG! I need to switch the variables.
5D = Q
I check: If I assume that I have 20 quarters, then 5D = 20
D = 4
Does this make sense? YES! I have 20 quarters and only 4 dimes.
Sometimes it helps to make a quick picture.
Imagine 2 piles of coins.
The pile of quarters is 5 times as high as the pile of dimes.
You can clearly see that you would need to multiply the number of dimes
to make that pile the same height as the number of quarters!

STRATEGY #3: MAKE A T-CHART
To translate known relationships to algebra (known as dimensional analysis), it often helps to make a T-Chart.
You always put the unknown variable on the LEFT side and what you know on the right.
Fill in the chart with 3 lines of numbers and look for the relationship between the 2 columns.
Then, you use that mathematical relationship with a variable.

EXAMPLE: The number of hours in d days
Your unknown is d days so that goes on the left side:
d days number of hours
1                   24
2                   48
3                   72
Now look at the relationship between the left column and the right column.
You must MULTIPLY the left column BY 24 to get to the right column
The last line of the chart will then use your variable d
d days number of hours
1                    24
2                   48
3                   72
d                  24d

EXAMPLE: The number of days in h hours (The flip of the first example)
Your unknown is h hours so that goes on the left side:
h hours number of days
24             1
48             2
72             3
(Why did I start with 24 and not 1 hour this time?)
Now look at the relationship between the left column and the right column.
You must DIVIDE the left column BY 24 to get to the right column
The last line of the chart will then use your variable h
h hours number of days
24           1
48           2
72           3
h        h/24
WHEN IT’S AN EQUATION AND NOT AN EXPRESSION….
You use the same strategies, but you’ll have an = sign and then you can solve for the unknown variable if there is only 1 variable:
10 less than the product of 5 and a number is 25:
5n – 10 = 25
n = 7

FORMulas
Equations that represent KNOWN RELATIONSHIPS are called formulas because there is a specific format that must be used that never changes.
For example, d = rt is a FORMula…it’s also an equation, but it has a more specific name because this is a KNOWN RELATIONSHIP in the real world.
You can translate words for formulas:
Distance is the product of the rate of speed and the time traveled.

TRANSLATING ALGEBRAIC EQUATIONS TO WORDS:
Going back the other way, you’ll have choices in the words you can use to represent the same equation.
2n = 40
You can say:
2 times a number is 40
Double a number is 40
Twice a number is 40
The product of a number and 2 is 40
The product of 2 and a number is 40 (multiplication is commutative!)