A certain computer program lets the user pick a positive number, decreases the number by 60%, and displays the square of the result. If the number displayed is 140% larger than the number that the user picked, what number did the user pick?
To find the number that the user picked, let's break down the problem step by step:
1. Let's assume the number that the user picked is "x".
2. The computer program decreases the number by 60%. Decreasing a number by 60% means multiplying it by (1 - 0.6), which is 0.4. So, the result of this step is 0.4x.
3. The program then displays the square of the result from step 2. So, the displayed number is (0.4x)^2, which simplifies to 0.16x^2.
4. According to the problem, the displayed number is 140% larger than the number the user picked. Increasing a number by 140% means multiplying it by (1 + 1.4), which is 2.4. So, we have the equation:
0.16x^2 = 2.4x
5. Now, we can solve the equation. Let's rearrange it:
0.16x^2 - 2.4x = 0
6. Factoring out x, we get:
x(0.16x - 2.4) = 0
7. So, x = 0 (which is not a positive number) or (0.16x - 2.4) = 0
8. Solving the equation (0.16x - 2.4) = 0, we find:
0.16x = 2.4
x = 2.4 / 0.16
x = 15
Therefore, the number that the user picked is 15.