Question

Use simultaneous equations to solve the following questions.


1. The denominator of a fraction is 1 less than 3 times the numerator. If the numerator and the denominator are both increased by 2, the fraction becomes $\frac{1}{2}$. Find the original fraction.
2. The value of a two-digit positive integer is 3 times the sum of two digits. If 9 is added to the two-digit integer, the new value will be 4 times the sum of the 2 digits of the original integer. Find the original two-digit integer.
3. Six years ago, the ratio of the age of Daniel to that of Fred was 5:2. Two years from now on, the ratio of the age of Daniel to that of Fred Will become 7:4. Find the present ages of Daniel and Fred.

Answer 1

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