If x + 0.4y = 3 and y = \;1/2x, find the value of (x + y)

Correct Answer is : 3 34\;3/443

Correct Answer is : 3 34\;3/443

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WAEC Mathematics 2012 Paper

Question : 22

Total: 49

\;\frac{1}{2}

x, find the value of (x + y)

Solution:

Concept:

Use substitution to solve the system of equations, then find the required sum.

Explanation:

Given

x + 0.4y = 3

and

y = \frac{1}{2}x

Substitute

y = \frac{1}{2}x

into the first equation.

x + 0.4\left(\frac{1}{2}x\right) = 3

x + 0.2x = 3

1.2x = 3

x = \frac{3}{1.2} = \frac{30}{12} = \frac{5}{2} = 2.5

Then

y = \frac{1}{2}x = \frac{1}{2} \times \frac{5}{2} = \frac{5}{4} = 1.25

Now find

x + y

x + y = \frac{5}{2} + \frac{5}{4}

Convert to a common denominator:

\frac{10}{4} + \frac{5}{4} = \frac{15}{4}

\frac{15}{4} = 3\frac{3}{4}

Answer:

x + y = 3\frac{3}{4}

Therefore, the correct option is C.

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