If x 0 4y 3 and y frac 1 2 x find the value of ... - WAEC Mathematics 2012 Question
If x + 0.4y = 3 and y = \(\frac{1}{2}\)x, find the value of (x + y)
A
1\(\frac{1}{4}\)
B
2\(\frac{1}{2}\)
C
3\(\frac{3}{4}\)
D
5
correct option: c
x + 0.4y = 3...(i)
y = \(\frac{1}{2}\)x
x = 2y
x - 2y = 0....(ii)
solve simultaneously; x + 0.4y
= 3 - x - 2y = 0
2.4 = 3
y = \(\frac{3 \times 10}{2.4 \times 10} \)
= \(\frac{30}{24} = \frac{5}{4}\)
x - 2(\(\frac{5}{4}\)) = 0
x - \(\frac{5}{2}\) = 0
x = \(\frac{5}{2}\)
x + y = \(\frac{5}{2} + \frac{5}{4}\)
\(\frac{10 + 5}{4} = \frac{15}{4}\)
= 3\(\frac{3}{4}\)
y = \(\frac{1}{2}\)x
x = 2y
x - 2y = 0....(ii)
solve simultaneously; x + 0.4y
= 3 - x - 2y = 0
2.4 = 3
y = \(\frac{3 \times 10}{2.4 \times 10} \)
= \(\frac{30}{24} = \frac{5}{4}\)
x - 2(\(\frac{5}{4}\)) = 0
x - \(\frac{5}{2}\) = 0
x = \(\frac{5}{2}\)
x + y = \(\frac{5}{2} + \frac{5}{4}\)
\(\frac{10 + 5}{4} = \frac{15}{4}\)
= 3\(\frac{3}{4}\)
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