Logic Math Word Problems?

Question

Draw a Venn diagram to help you solve these problems. (optional)

1. The Barksalot Pet Clinic did a study of 75 dogs brought in for treatment. It found that 40 of the dogs had fleas, 27 had ticks, and 14 had both. How many dogs had fleas but not ticks? How many dogs had ticks but not fleas?

2. Tom asked 100 adults whether they had ever collected stamps, coins, or baseball cards. 16 collected stamps, 7 collected coins, 22 collected cards, 4 collected cards and stamps, 1 collected coins and cards, 5 collected stamps and coins, and 5 collected all. How many had collected coins but not baseball cards? How many had collected baseball cards but not stamps?

3. Teresa asked students in her math class whether they owned a dog, a cat, or a bird. Of the 32 students surveyed, 12 owned a dog, 7 owned a cat, 9 owned a bird, 2 owned a dog and a cat, 3 owned a dog and a bird, 3 owned a cat and a bird; 1 student owned all three. How many students owned both a dog and cat but not a bird? How many students owned both a bird and a dog but not a cat?

Please explain clearly and thoroughly.

Thanks for helping me!

Answer 1

1. Let x be the number of dogs that had only ticks.

x = All dogs that have ticks  - dogs that had both

   = 27 - 14

   = 13

2. Let x be the number of adults that collected coins but not baseball cards.

x = All coin collectors - coins & card collector - all collector

   = 7 - 1 - 5

   = 1

Let y be the number of adults that collected cards but not stamps.

x = All card collectors - stamp & card collector - all collector

   = 22 - 4 - 5

   = 13

3. Let x be the number of students who owned both a bird and a dog but no cat.

x = People who owned a bird and a dog - People who owned all

   = 3 - 1

   = 2

Answer 2

1)  26 had fleas but not ticks

    13 had ticks but not fleas

I may be wrong though..  I did this like 100 years ago, so don't quite remember that well.  By the way, I'm 19 years old.  How old do you reallly think I am?  Logic question

Now, I'm working on 2 and 3