SOLUTION: Farmer Bill has a mixture of black and white sheep, with some being younger than 3 years and some being 3 years or older. His records indicate that there is a total of 80 sheep wit

Question 1202745: Farmer Bill has a mixture of black and white sheep, with some being younger than 3 years and some being 3 years or older. His records indicate that there is a total of 80 sheep with 28 being aged under 3 years and 30 sheep in total are black. There are 34 white sheep aged 3 years or more. Construct a two-way table to represent the data.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer

	White	Black	Total
Less than 3 yrs	16	12	28
3 yrs or older	34	18	52
Total	50	30	80

Explanation:

We have these given facts

There is a total of 80 sheep
with 28 being aged under 3 years
and 30 sheep in total are black.
There are 34 white sheep aged 3 years or more.

Fact 1 will mean 80 goes in the bottom right corner.
This is the grand total.

Fact 2 says that "28" goes at the end of the first row.
Then we combine facts 1 and 2 so we can determine the missing value in the final column is 80-28 = 52.

Fact 3 is then used to write "30" at the bottom of the second column.
The total for the other column must be 80-30 = 50 (when combining facts 1 and 3).
There are 50 white sheep and 30 black sheep to have 50+30 = 80 total.

Fact 4 then is used to write "34" just above the 50 we wrote earlier.
The remaining white sheep count is 50-34 = 16.

There are 16 white sheep aged less than 3 yrs, and 28 sheep of this age group. The remaining sheep of this age group must be 28-16 = 12.

The final slot must be 18 because either
30-12 = 18
or
52-34 = 18

Let me know if you have further questions.

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