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increase 120 in the ratio 3:2

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To increase a number in the ratio of 3:2, you first need to find what part of the number corresponds to each part of the ratio.

  1. Sum of the ratio parts:

    • \(3 + 2 = 5\)

  2. Finding the individual parts:

    • The "3" part corresponds to \( \frac{3}{5} \) of the total after the increase.
    • The "2" part corresponds to \( \frac{2}{5} \) of the total after the increase.

  3. Finding the new total:

    • Let \( x \) be the final total after the increase. We have:
    • The part that corresponds to the increase in the ratio (3 parts) is \( \frac{3}{5} \) of \( x \), and the original amount (120) corresponds to the \( \frac{2}{5} \) part.

  4. Setting up the equation:

    • \(\frac{2}{5}x = 120\)

  5. Solving for \( x \): \[ x = 120 \times \frac{5}{2} = 120 \times 2.5 = 300 \]

Thus, when you increase 120 in the ratio 3:2, the new total is 300.