If (x+2)/2=y/5, then which of the following must be true?
x/2=(y-2)/5
x/2=(y-5)/5
(x+2)/5=y/25
cross-multiply:
5(x+2) = 2y
5x + 10 = 2y
5x = 2y - 10
5x/2 = y - 5
x/2 = (y-5)/5
To determine which of the given options must be true based on the given equation, let's solve the equation (x+2)/2 = y/5 for x and y.
First, cross-multiply the equation to eliminate the fractions:
5(x+2) = 2y
Expand the multiplication:
5x + 10 = 2y
Now, let's analyze each option:
a) x/2 = (y-2)/5: This option comes from rearranging the given equation. However, we just found that 5x + 10 = 2y, not (y-2). Therefore, this option is not true.
b) x/2 = (y-5)/5: This option is also derived by rearranging the given equation. However, it does not match 5x + 10 = 2y. So, this option is not true either.
c) (x+2)/5 = y/25: This option is obtained by dividing both sides of the original equation by 2, giving (x+2)/5 = y/10. However, that is not what we found. Therefore, this option is not true.
None of the given options can be concluded based on the given equation.