Answer:
Q6
(i) 6x + 320
(ii) 9x = 540
(iii) $500
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Q7
(i) 12 years
(ii) 24 years
Explanation:
(For ease of writing, I am omitting $ signs until the very end)
Q6
We are told to denote the unknown value of a chair using the variable x.
We are also given that the the price of a dining table (unknown) is 320 more than 3 times the price of a chair
Lets denote the price of the dining table by the variable y
The statement 320 more than 3 times the price of a chair can be broken down and expressed in algebraic terms as follows:
-- 3 times the price of a chair is 3x
-- 320 more than 3 times the price of a chair is the same as 320 more than 3x ==> 320 + 3x
Since this is the price of the dining table for which we have used the variable y we get the equation:
y = 320 + 3x ........... (1)
Ans (i): 320 + 3x. It is convention to represent this as 3x + 320
(ii)
Chua paid 860 dollars for 1 dining table and 6 chairs
Since 1 dining table costs y dollars and each chair costs x dollars, we get a second equation:
6x + 1y = 860
We usually omit the leading coefficient so the above becomes
6x + y = 860
Since we have represented y using the expression 3x + 320 this becomes:
6x + (3x + 320) = 860
→ 6x + 3x + 320 = 860
→ 9x + 320 = 860
Subtract 320 from both sides to get
9x + 320 - 320 = 860 - 320
9x = 540
x = 540/9 = 60 which is the price of a chair
The price of a dining table from equation (1) becomes
y = 3x + 320 = 3(60) + 320 = 180 + 320 = 500
So the price of a dining table is $500 (Answer (iii)
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Q7
You have already used variable x to represent Mrs. Wong's age so we will stick to that
Let us represent Kate's current age using variable y
Today Kate is one-third as old as Mrs. Wong:
y = x/3
After 6 years, Kate will be y + 6 years = x/3 + 6 years
Mrs Wong will be x + 6 years
Sum of their ages in 6 years = x + 6 + x/3 + 6 and we are told this is 60 years
So the expression for sum of ages in 6 years becomes
x + 6 + x/3 + 6 = 60
x + x/3 + 12 = 60
Subtract 12 from both sides;
x + x/3 = 60 -12 = 48
x + x/3 = 4x/3
So
4x/3 = 48
Multiply by 3 both sides ==> 4x = 3 · 48
==> 4x = 144
Divide by 4 both sides:
x = 144/4
x = 36
This is Mrs. Wong's age now
Kate's age = 1/3 (36) = 12 years Ans(i)
(We can verify this by noting that after 6 years Kate's age is 12 + 6 = 18, Mrs. Wong's age is 36 + 6 = 42 and the sum of 18 and 42 is 60)
Ans(ii)
Since Kate is 12 years old, when Kate was born Mrs. Wong's would have been 12 years younger so her age would be 36 - 12 = 24 years