# Ratios and Proportions

### This week’s topic has been Ratios and Proportions.

Let’s go through that blue SAT book everyone has, http://amzn.to/1wADKLS, or http://amzn.to/1wtPZuD, and this ACT book for problems about ratios that can be solved using my TI-84 Plus programs RATIO and PROPORTN.  (See these posts for examples: 10/27, 10/28, 10/29, 10/30)

Sorry, I won’t post the actual problems here.  But go dig out your books and calculator (buy them here: SAT, ACT , TI-84 Plus) and follow along.

## SAT book

ISBN-13: 9780874478525.  The page numbers included here are from that book, but if you have the other one (9780874479799), please refer to the Test number and Section number instead.

Test 1, Section 7, p. 417, problem # 13

Test 4, Section 6, p. 594, problem #6

Test 10, Section 2, p. 953, problem #16

Test 10, Section 8, p. 980, problem #12

Math Multiple-Choice Sample Questions, p. 307, problem #6

Math Student-Produced Response Sample Questions, p. 347, problem #1

Test 1, Section 7, p. 417, problems # 11, 13

Test 2, Section 2, p. 452, problem #2

Test 3, Section 5, p. 528, problem #9

Test 3, Section 8, p. 543, problem #1

Test 4, Section 3, p. 583, problem #6

Test 5, Section 2, p. 639, problem #5

Test 6, Section 4, p. 715, problem #10

Test 7, Section 3, p. 768, problem #1

Test 9, Section 8, p. 916, problem #4

Test 9, Section 8, p. 918, problem #11

Test 10, Section 2, p. 950, problem #7

## ACT book

I’m working out of an older edition that only has 3 tests.  I believe they are the same as the first 3 tests of the 2nd and 3rd editions.  Once I have the newer book, I’ll add to this list.

Test 2, Section 2, problem #15

Test 1, Section 2, problems #19, 39, 44

Test 2, Section 2, problems #3

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# Ratios

Q: Last month, the ratio of sunny days to rainy days was 3:2.  How many rainy days  were there last month, if the month had 30 days?  (Assume all days were either sunny or rainy.)

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Solution by hand:

Number of sunny days = 3x

Number of rainy days = 2x

3x + 2x = 30

5x=30

x = 6

There were 2x rainy days, so there were 12 rainy days.

Solution using my TI-84 Plus Program RATIO:

Run RATIOHow?

Total number of items (days) = 30

Number of categories of items = 2  (sunny and rainy)

Ratio part for category 1 (sunny) = 3

Ratio part for category 2 (rainy) = 2

Distribution is: sunny = 18 and rainy = 12.

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# Proportions

### Q:  x is inversely proportional to w.  If x = 6 when w = 8, what is x when w = 12?

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Solution by hand:

For inverse proportions, (x1)(w1) = (x2)(w2)

(6)(8) = (x)(12)

48 = 12x

x=4

Solution using my TI-84 Plus Program PROPORTN:

Run PROPORTN.  How?

x1 = 6

y1 = 8  (here, we have renamed w1 as y1)

Have y2 (really w2)

y2 = 12

Choose ‘Inverse’ proportion.

Then, x2 = 4.

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# Proportions

### Q:  Wandering around blindly in a parking lot (don’t try it, please), the probability that the first car you bump into is blue is 2/5.  If there are 500 blue cars, how many cars are in the parking lot?

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Solution by hand:

Set up the proportion using the concept ‘blue / total = blue / total’:

2/5 = 500/x

2x = 2500

x = 1250

Solution using my TI-84 Plus Program PROPORTN:

Run PROPORTN.  How?

x1 = 2  (blue)

y1 = 5  (total)

Have x2 (blue)

x2 = 500

Choose ‘Direct’ proportion (because it doesn’t say ‘inverse’ in the problem).

Then, y2 (the total) = 1250.

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# Ratios

### Q:  The ratio of blue cars to non-blue cars in the parking lot is 2:7.  If there are 1260 cars in the parking lot, how many are blue?

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Solution by hand:

Number of blue cars = 2x

Number of non-blue cars = 7x

2x + 7x = 1260

9x=1260

x = 140

There are 2x blue cars, so there are 280 blue cars.

Solution using my TI-84 Plus Program RATIO:

Run RATIOHow?

Total number of items = 1260

Number of categories of items = 2  (blue and non-blue)

Ratio part for category 1 (blue) = 2

Ratio part for category 2 (non-blue) = 7

Distribution is: blue = 280 and non-blue = 980.

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# TI-84 Plus Programs

My TI-84 Plus programs are now available here.  Instructions and examples for each of the 40 programs are there so you can learn how and when to use them.  I’m in the process of cross-indexing them with the problems posted here.  Check back often and ask me questions!

You know that SAT book everyone has?  The blue one:  This one, or this one.  I’m about to start going through it page by page, pointing out the problems that can be solved using my programs.  Stay tuned!

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# Get a TI-84 Plus Calculator!!

## The BEST thing you can do to improve your SAT or ACT Math score is to get the TI-84 Plus calculator… and load it up with my programs.

It’s only \$108 today on Amazon, with free shipping! This is the best deal I’ve seen. By comparison, Walmart has it for \$119.27. Get it now: http://amzn.to/1vUA1IP

The TI-84 Plus is a great help to anyone taking the SAT or ACT. I have dozens of programs that will solve many typical problems in mere seconds. I can transfer these programs to your TI-84 Plus if you come to my office. BUT very soon they will be available for download on my website, with instructions and examples, so stay tuned!

By the way, there is no need to get any of the other fancier versions of this calculator. They won’t help you any more than this one does. But if you do want a certain color, well here are the other options:  http://amzn.to/1yi4bKd

(Yes, the TI-83 Plus is compatible with the programs, too, so that’s another option as listed in the above link, but the USB cable must be purchased separately.)

If all you need is the USB cable, here it is:

USB cable for  TI-84 Plus: http://amzn.to/1xAchur

USB cable for TI-83 Plus: http://amzn.to/1qAmCRx (Don’t buy the one above if you have the 83!!)

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# SAT – Probability

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### A: 1/10,000

Explanation:  Each digit is chosen from the integers 0 through 9, which is ten possible choices for each digit.  There are four digits to choose independently, so there are:

10 x 10 x 10 x 10 = 10,000 ways to choose the four digits.

Then, the one correct sequence of 4 digits, is one out of 10,000.  The probability is 1/10,000.

Another way to arrive at the number 10,000 is as follows:

The 4-digit sequence may be anything from 0000 to 9999.  So, how many is that?  9999 – 0000 +1 = 10,000.  Why the ‘plus one’ on the end?  If you just subtract the numbers, it tells you how many spaces there are between the numbers.  Add one to include either the first number or the last number, whichever one has not been already counted.