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Question 71237This question is from textbook Algebra 1
: Hi, thank you for taking your time to help me. There is problem #17. In Lewis Carroll's Through the Looking Glass, Tweedledum says to Tweedledee, "The sum of your weight and twice mine is 361 pounds. Then Tweedledee says to Tweedledum, "Contrariwise, the sum of your weight and twice mine is 362 pounds.Find the weight of Tweedledum and Tweedledee
#18. During a publicity campaign, a cycle shop gave away 5000 miniature cycles and bumper stickers. The cycles cost .63 each and the bumper stickers cost .52 each. The cycle shop spent $2798 on the gifts. How many of each gift did he buy?
#20.Solve the problem below. Then write an argument that would convince a classmate that your solution is correct.
Several ancient Chinese books include problems that can be solved by translating to systems of equations. Arithmetical Rules in Nine Sections was compiled by Chang Tsang, a Chinese matematician who died in 152 B.C. One of the problems is:Suppose there are a number of rabbits and pheasanta confined in a cage. In all, there are 35 heads and 94 feet. How many rabbits and how many pheasants are there?
I tried to guess and check for this one..but I couldn't figure anything out & my teacher wanted us to try and write equations for the problems..but I can't find no other way then guess and check. Thanks again for your help!
This question is from textbook Algebra 1
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! #17.
Let x = the weight of Tweedledum and y = the weight of Tweedledee.
According to Tweedledum:
1) 
According to Tweedledee:
2) 
Now we have a system of equations with two unknowns and this system can be solve for x and for y.
We'll use the elimination method so we multiply equation 1) by 2:
1a) 
Now we'll subtract equation 2) from equation 1a) to eliminate the y
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 Divide both sides by 3.
 So Tweedledum weighs 120 lbs.
Now back to equation 1) where we substitute x = 120 and solve for y.
 Simplify.
 Subtract 240 from both sides.
 Tweedledee weighs 121 lbs.
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#18
Let C = the number of miniature cycles and S = the number of bumper stickers.
1) C + S = 5,000 The sum of the cycles and stickers is 5,000
2) ($0.63)C + ($0.52)S = $2,798.00
Here we can use the substitution metod to solve this system of equations.
Rewrite equation 1) as:
1a) C = 5,000-S and substitute this for C in equation 2)
2a) 0.63(5000-S)+(0.52)S = 2,798 Simplify and solve for S
3150-0.63S+0.52S = 2,798 Simplify.
3150-0.11S = 2,798 Subtract 3150 from both sides.
-0.11S = -352 Divide both sides by -0.11
S = 3,200 This is the number of bumper stickers.
C = 5,000-3200
C = 1,800 This is the number of miniature cycles.
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#20
Let R = the number of rabbits and P = the number of pheasants.
Since both rabbits and pheasants have but one head each, then:
1) R+P = 35
Rabbits have four legs each while pheasants have two legs each, so we can write the total number of legs as:
2) 4R+2P = 94
Rewrite equation 1) as:
1a) R = 35-P Now multiply this equation by 4 to get:
1b) 4R = 140-4p and substitute this for 4R in equation 2, then solve for P.
2a) 140-4P+2P = 94 Simplify.
140-2P = 94 Subtract 140 from both sides.
-2P = -46 Divide both sides by -2.
P = 23 There are 23 pheasants.
R = 35-P
R = 35-23
R = 12 There are 12 rabbits.
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