A simultaneous equation can be written based on the word problem and
from which the numbers can be found.
Reasons:
The given parameters are;
The sum of two numbers = 130
The sum of the first number increased by 10% and the second number
increased by 40% = 161
Let A and B represent the number, we have;
A + B = 130...(1)
A·(1.10) + B·(1.40) = 161...(2)
Multiplying equation (1) by 1.1, and subtracting it from equation (2) gives;
A·(1.10) + B·(1.40) - ((1.1) × (A + B)) = 161 - 1.1× 130
0.3·B = 18
B = 60
From equation (1), we have;
A = 130 - B
Which gives;
A = 130 - 60 = 70
A = 70
The numbers are 60 and 70
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