The key to solving word problems is DON’T BE SCARED.
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Transcript of 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
Proportion An equation that says two
fractions (or ratios) are equal
Proportion An equation that says two
fractions (or ratios) are equal
Proportion An equation that says two
fractions (or ratios) are equal
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
Similar figures Same shape, but different
sizes
Similar figures Same shape, but different
sizes
Similar figures Same shape, but different
sizes
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?
15% of what number is 82?
_The answer is 546.6 .
8 is what percent of 128?
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?
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.
A pair of jeans that normally costs $59 is on sale for $35.40. What is the percent of decrease?
59 – 35.4 = 23.6
A pair of jeans that normally costs $59 is on sale for $35.40. What is the percent of decrease?
59 – 35.4 = 23.6
A pair of jeans that normally costs $59 is on sale for $35.40. What is the percent of decrease?
59 – 35.4 = 23.6
The jeans are 40% off.