Question

Leila says that 75% of a number will always be greater than 50% of any other number. Complete one inequality to support Leilas claim and one to show that she is incorrect

Answer 1

Support

75% of 50 >  50%  of 2

Refute

75% of 2< 50% of 22

Answer 2

If a number is positive, Leila's theory that 75% of a number will always be greater than 50% of another number is true; however, if both numbers are negative, or if the number of which she finds 50% is much greater than the number of which she finds 75%, Leila's theory could be incorrect.

This inequality shows that Leila is correct: $100(0.75) \geq 50(0.50)$ (which simplifies to $75 \geq 25$)

This inequality shows that Leila is incorrect: $50(0.75) \geq 100(0.50)$ (which simplifies to $37.5 \geq 50$)

Hope this helps!