Page 20 - Algebra 1

P. 20

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The fraction becomes 𝑥 12−𝑥
On adding 3 to the numerator and subtracting 5 from the denominator
𝑥+3 =4 12−𝑥−6 5
5(x + 3) = 4(6– x)
5x + 15 =24 – 4x
5x + 4x = 24– 15
9x = 9 x=1
7.
Fraction= 𝑥 =1 12−𝑥 11
or even from the answers you can deduce 1 because when you add 3 to the numerator and 11
subtract 6 from the denominator you get 4 5
Let the age of Julie 14 years be x
Age of the grandmother 14 years ago = 10x
Present age of Julie = x + 14
Present age of the grandmother = 10x + 14
Age of Julie 6 years from now = x + 14 + 6 = x + 20
Age of the grandmother 6 years from now = 10x + 14 + 6 = 10x + 20
As per the question,
10x + 20 = 4(x + 20)
10x + 20 = 4x + 80
6x = 60
x = 10
P and Q are two non-empty sets such that P{𝑎, 𝑏}, Q {1, 4, 5}, then P × Q = {(𝑎,1),(𝑎,4),(𝑎,5),(b,1),(b,4),(b,5)},
Q × P = {(1,𝑎),(4,𝑎),(5,𝑎),(1,b),(4,b),(5,b)}
This is the Cartesian product of two non-empty sets.
Therefore, if P and Q are two non-empty sets, then the subset of P × Q is also the relation from P to Q.
For example,
P = {𝑎,𝑏}, Q = {1,4,5}
Then {(𝑎, 1), (𝑎, 4), (𝑏, 5)} is a relation in P × Q. There will be many more relations in P × Q.
Present age of Julie = x + 14 = 10 + 14 = 24 years
Present age of the grandmother = 10x + 14 = 100 + 14 = 114 years
Ratio= 24 = 4 or4:19 114 19
Page 19 of 54
ALGEBRA
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