SOLUTION: . The cost of four chairs and a small table is $648. The cost of six chairs and a large table is $1 196. The cost of the large table is Twice the cost of the small table. Given th

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Question 1190214: . The cost of four chairs and a small table is $648. The cost of six chairs and a large table is $1 196.
The cost of the large table is Twice the cost of the small table. Given that a is the cost, in dollars, of a
chair and b is the cost, in dollars, of a small table
(i) write a pair of simultaneous equations to represent the information given. (2mks)
(ii)calculate the cost of a chair and the cost of a large table.
Found 3 solutions by math_tutor2020, greenestamps, MathTherapy:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

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:
4a+b = 648
6a+2b = 1196

====================================================

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 = $50
One large table = $896
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


I will use the same start as the other tutor but solve by a different method....

a = cost of a chair
b = cost of a small table
2b = cost of a large table (twice the cost of a small table)

4a+b=648 the cost of 4 chairs and a small table is $648
6a+2b=1196 the cost of 6 chairs and a large table is $1196

When the two equations are both in Ax+By=C form, I think elimination is far easier than substitution....

8a+2b=1296 (double the first equation)
6a+2b=1196
2a=100 (subtract the two equations)
a=50

4(50)+b=648
200+b=648
b=448
2b=896

ANSWERS:
chair: a=$50
large table: 2b=$896
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

. The cost of four chairs and a small table is $648. The cost of six chairs and a large table is $1 196.
The cost of the large table is Twice the cost of the small table. Given that a is the cost, in dollars, of a
chair and b is the cost, in dollars, of a small table
(i) write a pair of simultaneous equations to represent the information given. (2mks)
(ii)calculate the cost of a chair and the cost of a large table. 
With "a" and "b" being the cost of a chair and a small table, respectively, the cost of a large table = 2b
We then get: 4a + b = 648 ------ eq (i)
Also, 6a + 2b = 1,196____2(3a + b) = 2(598)___3a + b = 598 ----- eq (ii)
Cost of a chair, or  ----- Subtracting eq (ii) from (i)

6(50) + 2b = 1,196 ------ Substituting 50 for a in eq (ii)
Cost of a large table, or 2b = 1,196 - 6(50) = 1,196 - 300 = $896
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