t.martinez
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In a flock of sheep 2 out of 5 are white. If there are 8 more black sheep than white, how many sheep are in the flock?
Sheep: 2 of 5 are white; if 8 more black, how many total?
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Re: Sheep
It appears that you have two rather straight forward statements and two unknowns. You don't say what method you want to use to solve. I will assume you can use two equations in two unknowns.
First step is to name things. You really have three unknowns---the number of white sheep, the number of black sheep and the size of the flock. Well, the size of the flock is the sum of the whites and the blacks, so we really only need to build our equations using two unknowns. When naming things, write down what you are naming...
Let b represent the number of black sheep.
Let w represent the number of white sheep.
Now, translate the statement "there are 8 more black sheep than white", into an equation.
Do you see that this statement is saying "The number of black sheep is eight more than the number of white sheep"? Maybe that is easier to write an equation from.
The other statement to use to form an equation is "In a flock of sheep 2 out of 5 are white." Be careful, here. This is saying that for every 2 white sheep there are 3 black sheep. I would build a proportion to represent this statement. My proportion would look like this...
\(\displaystyle \frac{b}{w}=\frac{?}{?}\) where different numbers replace the question marks.
Now, hopefully, you have one linear equation in b and w and one proportion in b and w. Go ahead and solve those simultaneously. When you solve for w and b, remember that the question asks for the total number of sheep. Be sure to check you answers back in the words of the original question.
It appears that you have two rather straight forward statements and two unknowns. You don't say what method you want to use to solve. I will assume you can use two equations in two unknowns.
First step is to name things. You really have three unknowns---the number of white sheep, the number of black sheep and the size of the flock. Well, the size of the flock is the sum of the whites and the blacks, so we really only need to build our equations using two unknowns. When naming things, write down what you are naming...
Let b represent the number of black sheep.
Let w represent the number of white sheep.
Now, translate the statement "there are 8 more black sheep than white", into an equation.
Do you see that this statement is saying "The number of black sheep is eight more than the number of white sheep"? Maybe that is easier to write an equation from.
The other statement to use to form an equation is "In a flock of sheep 2 out of 5 are white." Be careful, here. This is saying that for every 2 white sheep there are 3 black sheep. I would build a proportion to represent this statement. My proportion would look like this...
\(\displaystyle \frac{b}{w}=\frac{?}{?}\) where different numbers replace the question marks.
Now, hopefully, you have one linear equation in b and w and one proportion in b and w. Go ahead and solve those simultaneously. When you solve for w and b, remember that the question asks for the total number of sheep. Be sure to check you answers back in the words of the original question.
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Of every five, how many are white? Of every five, how many are black? How many more black sheep is this than white sheep, in every five?t.martinez said:
If you need eight more black sheep in total, then how many sets of five sheep do you need?
How many sheep are in this many sets of five sheep?
Eliz.
Hello, t.martinez!
Let \(\displaystyle N\) = number of sheep in the flock.
\(\displaystyle \text{"Two out of five are white": }\;\tfrac{2}{5}N \text{ white sheep.}\)
. . . \(\displaystyle \text{Then the rest is black: }\;\tfrac{3}{5}N \text{ black sheep.}\)
\(\displaystyle \text{"8 more black than white": }\;\tfrac{3}{5}N \;=\;\tfrac{2}{5}N + 8\)
\(\displaystyle \text{Now solve for }N\;\hdots\)
Let \(\displaystyle N\) = number of sheep in the flock.
\(\displaystyle \text{"Two out of five are white": }\;\tfrac{2}{5}N \text{ white sheep.}\)
. . . \(\displaystyle \text{Then the rest is black: }\;\tfrac{3}{5}N \text{ black sheep.}\)
\(\displaystyle \text{"8 more black than white": }\;\tfrac{3}{5}N \;=\;\tfrac{2}{5}N + 8\)
\(\displaystyle \text{Now solve for }N\;\hdots\)