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Question

this is for my geometry problem set I'm really having trouble and would appreciate the help. Thank you. Also if you could answer problems with picture I could use that also

 

chip said to dale, "if you give me one acorn, then we will have an equal number of acorns." Dale replied with delight, "If you give me one acorn, then I will have double the number you have!" What was the number of acorns each of them had

Answer 1

You can create the equation d-1=c+1 from the first sentence.  Then create another equation from the second sentence: d+1=2(c-1).  Next choose one of the equations and solve for one of the variables:

 

1st equation solving for d:

     d+1-1=c+1-1;     d=c+2

 

replace the this value for d in the second equation:

    (c+2)+1= 2(c-1)

    c+3=2c-2

 

(Which is the same as , and since I like to keep the variable on the left, I choose to flip this equation.)

 

2c-2=c+3

2c-c=3+2

c=5

 

Next replace this value of 5 for the c in the original 1st equation:

 

d-1=c+1

d-1=5+1

d=6+1

d=7

 

You can use these numbers to check your answers in the sentences:

 

If Dale has 7 acorns and he gives one to Chip, who has 5 acorns, they will have the same number of acorns.  

 

If Chip gives one of his acorns to Dale he will have 4 and Dale will have 8, which is twice the number as Chip.

 

 

 

    

     

Answer 2

Let's call Chip X and Dale Y.

When X gets 1 acorn from Y, it increased to X +1, and Y decreases to Y -1. But at that point they are supposed to be equal:

X+1 = Y - 1, thus X = Y - 2

Now if X gives Y an acorn, Y increases to Y + 1. But now the number of Dale's acorns is double those of Chip's AFTER giving up (-1) an acorn: 2(x - 1).

2(X-1) = Y + 1

2X -2 = Y + 1

Plug in Y-2 for X,

2(Y-2) - 2 = Y + 1

2Y - 4 -2 = Y + 1

2Y -6 = Y + 1

Y = 7

Pug in 7 for Y in X = Y - 2, and X = 5

Note that if X (Chip) gets an acorn fro m Y (Dale), X = 6 and Y = 6 (same number).

And if X gives an acorn to Y, X = 4 and Y = 8 (Y has double the number X has.)

Answer 3

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