If the first number is increased by 30% and the second number by 80%, the sum will be 1.6 times larger than the initial sum. Find the ratio of the first number to the second number.

2 : 3

Step-by-step explanation:

Let x represent the first number and let y represent the second number.

Therefore the initial sum of the numbers = x + y

Given that the first number is increased by 30%, it becomes = x + 30% of x = x + 0.3x = 1.3x.

Also, the second number is increased by 80%, it becomes = y + 80% of y = y + 0.8y = 1.8y.

The sum of this increased numbers is 1.6 times larger than the initial sum. That is:

1.3x + 1.8y = 1.6(x + y)

1.3x + 1.8y = 1.6x + 1.6y

1.8y - 1.6y = 1.6x - 1.3x

0.2y = 0.3x

The ratio of the first number to the second number (that is x / y) is:

0.3x = 0.2y

Divide through by 0.3y:

0.3x / 0.3y = 0.2y / 0.3y

x / y = 0.2 / 0.3

x / y = 2 / 3

x : y = 2 : 3

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step-by-step explanation:

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation: