Sheep: An Old Puzzle
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Two farmers, Fred and Violet, were taking their sheep to market. Fred said, "Give me one of your sheep so we will both have the same amount." Violet answered, "No! Instead, you better give me one of yours, so I’ll have twice as many as you have." How many sheep did each of them have? We will solve this problem using four boards, the first two boards representing the first equality, and the second two representing the second equality. V is the number of sheep that Violet has, and it is represented by the blue triangle counter; and F is the number of sheep that Fred has, represented by the green square counter. We represent Fred’s statement on the first two boards: "Give me one of your sheep so we will have the same number of sheep."
V - 1 = F + 1 Violet says, "No! Instead, you better give me one of yours, so I’ll have twice as many as you have." This is represented on the two B boards below.
V + 1 = 2F - 2 On the A boards, we can isolate variable counter V by adding one to both sides.
We regroup on both sides.
V = F + 2 Now that we know that V = F + 2, let's put it on the B boards.
F + 3 = 2F - 2 Now we regroup.
Now, let's do a lot of regrouping on the B boards to isolate the green square variable. We can subtract one green square variable from both sides.
F - 2 = 3 We regroup.
We add 2 to both sides and regroup.
So the green square variable has value 5. Fred has 5 sheep! Let's put that value for F in the A board at the top to get the value of the blue triangle variable, how many sheep Violet has.
V = F + 2
V = 7 So Violet has 7 sheep! Let's check it. V - 1 = F + 1 7 - 1 = 5 + 1 = 6. Check. V + 1 = 2F - 1 7 + 1 = 2*5 - 2 = 8. Check. Number Board index |
