Question

challenge #4
a number went into this machine and 57 came out.
what number went in?
image of a machine with two operations: increase by 50% and decrease by 5%

Explanation:

Step1: Define the input number

Let the number that went into the machine be \( x \).

Step2: Apply the first operation (increase by 50%)

Increasing \( x \) by 50% means we multiply \( x \) by \( 1 + 0.50 = 1.5 \). So after the first operation, the number becomes \( 1.5x \).

Step3: Apply the second operation (decrease by 5%)

Decreasing the result from Step 2 by 5% means we multiply \( 1.5x \) by \( 1 - 0.05 = 0.95 \). So the final number (which is 57) is given by the equation \( 0.95\times(1.5x)=57 \).

Step4: Solve the equation for \( x \)

First, simplify the left - hand side of the equation: \( 0.95\times1.5x=(0.95\times1.5)x = 1.425x \)
Now we have the equation \( 1.425x = 57 \)
To solve for \( x \), divide both sides of the equation by 1.425: \( x=\frac{57}{1.425} \)
Calculate \( \frac{57}{1.425}=40 \)

Answer:

40