posted by .

Santa was making up a batch of dolls but could not remember exactly how many of each kind he needed. He knew that he needed 57 in total that 27 had to have blue eyes and 29 had to have fair hair. Also some had to have both features and 3 dolls were needed having blue eyes and fair hair but were not able to say " I love math". Also santa needed a total of 34 dolls able to say " I love Math" of whom 17 needed to have fair hair. Every doll had at least 1 of sthe features named and there was one combination of features not asked for at all. Several children had asked for all 3 features in the one doll. How many fair-haired, blue -eyed dolls saying "I love math" were needed.

• 5th grade math word problem -

• 5th grade math word problem -

13. Here's why:

There are eight possible combinations, which I will refer to as A - H, as follows:

A. Blue, Fair, LoveMath
B. Blue, Fair, NotLoveMath
C. Blue, NotFair, LoveMath
D. Blue, NotFair, NotLoveMath
E. NotBlue, Fair, LoveMath
F. NotBlue, Fair, NotLove Math
G. NotBlue, NotFair, LoveMath
H. NotBlue, NotFair, NotLoveMath

Here are the clues:

1. He knew that he needed 57 in total,
2. that 27 had to have blue eyes
[2a. so 30 do not have blue eyes]
3. and 29 had to have fair hair.
4. His assistant gnome pointed out that some had to have both features
5. and remembered that 3 dolls were needed having blue eyes and fair hair, but which were not able to say 'I Love Math'.
6. he needed a total of 34 dolls able to say ''I Love Math',
7. of whom 17 needed to have fair hair [7a which means that 17 did not have fair hair].
8. "Every doll had at least 1 of the features named";
9. "That there was one combination of features not asked for at all"
10. "Several children had asked for all 3 features in the one doll".

From clue 5 you know B = 3
From clue 8 you know H = 0
From clue 3, A+B+E+F = 29. We already know B = 3, and from clue 7 A+E = 17. So F=9.
From clue 9 you know one of the remaining is 0. Let's guess that C=0 (you can try others, but this seems to work out)
Then from c7a, since C=0 that means G = 17.
From 2a, since E+F+G = 30 and already know F=9 and G=17, so E=4.
From 7, given E=4 then A = 13.
Finally from 2, since A+B+C+D = 30, then D=11.

So:
A = 13 = Blue, Fair, LoveMath

• 5th grade math word problem -

2588963

• 5th grade math word problem -

i don't know!!!!! waaaaaaahh!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

mommy? is that you? no!!!! its santa!

Similar Questions

one parent has brown eyes the other has blue eyes, if they have a child what is the percent that it will have brown eyes?
2. statistics

The first sample had 49 subjects and 7 had blue eyes. The second sample had 465 subjects and 244 of these had blue eyes. What is the value of the pooled estimate of the proportion used to test the hypothesis that the population proportions …

1) of the dolls in mo's doll collection, 1/5 have red hair. of these 3/4 have green eyes. what fraction of Mo's dolls collection have both red hair and green eyes?
4. math

There are x students in Mrs. Schwartz's third-grade class. One less than half the students have blue eyes. Six fewer children have green eyes than have blue eyes. The rest of the students have brown eyes. How many students have brown …
5. math

1. Elizabeth planned to make 6 pans of apple crisp for the day, using extra tart granny smith apples-just like her grandmother had. But after peeling, coring, and slicing she had a major problem: she only had 10 cups of apple slices. …
6. Math

Sarah was trying to figure out her grades for her math course. she only knew the grade of 4 of the tests she had taken, However the class had taken 5 tests total. She scored a 94, 67, 83, and 93. If Sarah ended up with a grade of 90, …
7. Statistics

Achusband and wife with brown eyes who have 0.75 probability of having children with brown eyes, 0.125 probability of having children with blue eyes, and 0.125 probability of having children with green eyes. (a) What is the probability …
8. math

1.Elizabeth planned to make 6 pans of apple crisp for the day, using extra tart granny smith apples-just like her grandmother had. But after peeling, coring, and slicing she had a major problem: she only had 10 cups of apple slices. …