Let's denote the smaller number as x and the larger number as y.

From the problem, we know that:

1) x + y = 650 (since the sum of the two numbers is 650)

2) y - 0.04y = x + 0.12x (since the bigger number decreased by 4% is equal to the smaller number increased by 12%)

We can simplify the second equation to:

0.96y = 1.12x

Now we have a system of two equations, and we can solve it step by step.

First, let's express y from the first equation:

y = 650 - x

Now we can substitute y in the second equation:

0.96 * (650 - x) = 1.12x

This simplifies to:

624 - 0.96x = 1.12x

Combine like terms:

2.08x = 624

Finally, solve for x:

x = 624 / 2.08

x = 300

So, the smaller number is 300.

Question

Let's denote the smaller number as x and the larger number as y.

From the problem, we know that:

1) x + y = 650 (since the sum of the two numbers is 650)

2) y - 0.04y = x + 0.12x (since the bigger number decreased by 4% is equal to the smaller number increased by 12%)

We can simplify the second equation to:

0.96y = 1.12x

Now we have a system of two equations, and we can solve it step by step.

First, let's express y from the first equation:

y = 650 - x

Now we can substitute y in the second equation:

0.96 * (650 - x) = 1.12x

This simplifies to:

624 - 0.96x = 1.12x

Combine like terms:

2.08x = 624

Finally, solve for x:

x = 624 / 2.08

x = 300

So, the smaller number is 300.

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