the key to solving word problems is don’t be scared

The key to solving word problems is DON’T BE SCARED.

Basic Algebra Problems• Read the problem, looking

for key words.• Write an equation, and

solve.• Make sure you answered

the question that was asked and your answer is reasonable.

Mailing an oversized letter in the USA costs 98 cents for the first ounce and 21 cents for each additional ounce. If a letter has $3.08 in postage on it, how much did the letter weigh?

98 + 21x = 308

or

.98 + .21x = 3.08

98 + 21x = 308or .98 + .21x = 3.08

Solving either of these, you get x = 10

CAREFUL: READ THE PROBLEM AGAIN:Mailing an oversized letter in the USA costs 98 cents for the first ounce and 21 cents for each additional ounce. If a letter has $3.08 in postage on it, how much did the letter weigh?

The 10 is the number of additional ounces, so the answer to the question is that the letter weighed 11 ounces.

Ratio = A comparison of specific things

Ratios can be written three ways:

3 to 5

3 : 5

3/5

You reduce ratios just like fractions.

15 : 20 or 3 : 4

A unit rate is the ratio of several of a first thing to ONE of another. miles per hour dollars per pound calories per serving

Remember … “per” means

If Grandma drives 182 miles in 3.5 hours, what is her average speed?

If Grandma drives 182 miles in 3.5 hours, what is her average speed?

182 3.5 = 52 miles per hour

A bottle of pop has 3.5 servings. There are 98 calories per serving. How many calories are in the whole bottle?

A bottle of pop has 3.5 servings. There are 98 calories per serving. How many calories are in the whole bottle?

98 = x 3.5 98 3.5 = 343 calories

Proportion An equation that says two

fractions (or ratios) are equal

We care about proportions when one of the parts includes a variable.

You can solve proportions by cross-multiplying.• Multiply diagonally, and

set equal.

… 21x = 2016 x = 96

x = 15You can just do 6 25 10

x = 21/8 or 2.625

3(2x + 3) = 63 6x + 9 = 63 6x = 54 x = 9

2(5x + 10) = 450x = 43

2(4x – 1) = 158x – 2 = 15 x = 17/8 or 2.125

Problems that use proportion:

When a car dealer sells a $19,000 car, he makes a profit of $2850. At the same rate, how much profit would he make on a $24,000 car?

x = $3600

The ratio of boys to girls in a class is 4 : 3. If there are 20 girls, how many boys are there?

x = 80/3 or 26.666

In practical terms, the answer would be 27 boys.

There were 36 problems on an assignment, and it took John 90 minutes to do the assignment. If the assignment only had 20 problems of similar difficulty, how long would it have taken John to do them?

x = 50 minutes

Similar figures Same shape, but different

sizes

The symbol for similar is ~ .

Corresponding lengths in similar figures are proportional.

x

30

2

3

h

18

9.

6

Percent Literally means

“out o100” You can solve any percent

problem using the proportion

You can identify the whole with the word “of”.

15% of what number is 82?

15% of what number is 82?

_The answer is 546.6 .

8 is what percent of 128?

8 is what percent of 128?

The answer is 6¼%

What is 13% of 520?

What is 13% of 520?

The answer is 67.6

A pair of jeans that normally costs $59 is on sale for $35.40. What is the percent of decrease?

FIRST – Find how much you save.

THEN – Find what percent that is of the original amount.


59 – 35.4 = 23.6


59 – 35.4 = 23.6

The jeans are 40% off.

the key to solving word problems is don’t be scared

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