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Let the two numbers be x and y, then:
- Twice the first equals three times the second: 2x = 3y
- Three times their difference exceeds the second by 13: 3(x - y) = y + 13
From equation (1) it is clear the first number (x) is greater than the second (y), so their difference is x - y.
Equation (2) can be rearranged:
3(x - y) = y + 13
→ 3x - 3y = y + 13
→ 3x = 4y + 13
This gives two simultaneous equations:
- 2x - 3y = 0
- 3x - 4y = 13
which can then be solved to find the two numbers (x and y).
What else can I help you with?
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