# Beginning Algebra Tutorial 9

Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 9: Reading Graphs

Answer/Discussion to 1a - 1c

1a.  About how much was the profit in September?

The bar that associates with September is the first bar on the left.  The top of that bar is in between 5 and 10 on the vertical axis.  A good approximation is 8.

The profit in September is about \$8000.

1b.  Which month had the highest profit?

It looks like December had the highest profit.

1c.  What is the difference between the profits of October and November?

The bar that associates with October is the second bar from the left.  The top of that bar matches with 5 on the vertical axis.

The bar that associates with November is the third bar from the left.  The top of that bar matches with 10 on the vertical axis.

The difference between the profits of October and November would be 10,000 - 5,000 = \$5,000.

Answer/Discussion to 2a - 2c

2a.  How much was Thursday's high temperature?

The point that matches with Thursday on the horizontal axis also matches 80 on the vertical axis.

Thursday's high temperature was 80 degrees Fahrenheit.

2b.  Which day had the lowest high temperature?

It looks like Saturday had the lowest high temperature.

2c.  What temperature occurred the most?

It looks like 85 degrees Fahrenheit occurred three times which is the most.

Answer/Discussion to 3a - 3c

3a.  What was the ratio between male gym members and female gym members in 2000?

When setting up a ratio you need to write the number that corresponds to the first part first and then compare it to the number that corresponds to the second part of the ratio.

What do you think the first part of the ratio is, males or females?  Since males are listed first, that is what our first number of our ratio has to correspond to.

What is the number attached to males gym members in 2000?  Looking at the solid line, I believe it is 50.

That leaves the number associated with females to be our second part of the ratio. Looking at the dashed line we get 15.

So the ratio of male gym members to female gym members in 2000 would be 50 to 15.

You can think of ratios as fractions, and simplify them in the same manner.  Since 50 and 15 have a greatest common factor of 5, we can reduce this to be 10 to 3.

The reduced ratio of male gym members to female gym members is 10 to 3.

Note that if you had started with 15 to 50, this would be incorrect.  15 to 50 would be the ratio of females to males.  You write a ratio, just like you read it, left to right.

3b.  For what year shown on the graph did male gym membership not change from the year before?

Are we going to look at the solid or dashed line for this question?  Since we are only interested in the male membership, we will need to look at the solid line.

Going from left to right on the solid lines it appears that male membership goes up from 1998 to 1999 to 2000.  Then it goes down from 2000 to 2001.  But look how the line is horizontal from 2001 to 2002.  Male gym goers numbered 30 in both 2001 and 2002.

So the answer would be in 2002 male gym membership did not change from the previous year.

3c.  What was the total enrollment of the gym from 1998 to 2000?

Let’s break this down into female and male gym members.

Looking at the dashed line to see the number of females we get 20 + 20 + 15 = 55.

Looking at the solid line to see the number of males we get 40 + 45 + 50 = 135.

Putting those together we have 55 + 135 = 190 gym members from 1998 to 2000.

Answer/Discussion to 4a - 4c

A group of students were asked if they liked rock or country music.  The results were as follows: 27 said they liked rock, 20 said they liked country, 5 liked both, and 3 liked neither.

The first thing we need to do is draw a Venn diagram with two adjoining circles - one for rock and one for country.

Now we need to fill in numbers into the correct regions based on the information that was given.

We need to start with something that only goes with one region and then work our way out from that.

Two statements deal with only one region.  If more than one does, it doesn't matter the order you fill them in as long as they go with only one area.

It says that 5 liked both.  The only region that both circles meet in is region II, so we will have to put a 5 there.

Another statement that pertains to only one region is 3 like neither.  That means we will be putting the number 3 in region IV.

Let's put those into our Venn diagram and see what is left:

Looks like we still need to fill in regions I and III.

It says that 27 said they liked rock - the rock circle is composed of regions I and II.  Since II already had 5, then region I is going to have to be 27 - 5 = 22.

It also says that 20 said they liked country - the country circle is composed of regions II and III.   Since II already has 5, then region III is going to have to be 20 - 5 = 15.

4a. How many students chose only rock?

This would be region I.

The number of students that chose only rock is 22.

4b.  How many students chose only country?

This would be region III.

The number of students that chose only country is 15.

4c.  How many students were surveyed?

This would be regions, I, II, III, and IV.

To find the total we simply add up all the regions: 22 + 5 + 15 + 3 = 45

The number of students that were interviewed about rock and country is 45.