Question 1190214
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Part (i)


a = cost of one chair
b = cost of one small table
2b = cost of one large table (twice as much as the small table)
costs are in dollars


Since "The cost of four chairs and a small table is $648", we can say,
4a+b = 648


Since "The cost of six chairs and a large table is $1,196", we can say,
6a+2b = 1196


Answer: 
<font color=red>4a+b = 648
6a+2b = 1196</font>


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Part (ii)


Solve for b in the first equation
4a+b = 648
Isolating b gets us
b = 648-4a


Then plug that into the second equation and solve for 'a'.
6a+2b = 1196
6a+2(648-4a) = 1196
6a+1296-8a = 1196
-2a+1296 = 1196
-2a = 1196-1296
-2a = -100
a = -100/(-2)
a = 50


So,
b = 648-4a
b = 648-4*50
b = 648-200
b = 448 is the cost of a small table
and,
2b = 2*448 = 896 is the cost of a large table


Check:
4 chairs + 1 small table = 4*50 + 1*448 = 648
6 chairs + 1 large table = 6*50 + 1*896 = 1196
Both prices check out. The answers are confirmed.


Answer: 
One chair = <font color=red>$50</font>
One large table = <font color=red>$896</font>
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