Question

State whether the following statement is true or​ false, and explain why. If the statement is​ false, state the true change. The cost of tuition at a college falls by 14​%, then later rises by 14​%. After the two changes in tuition, the cost is unchanged. Is the statement true or false and what is the true change?

Answer 1

The statement is false; tuition does not return to the original amount after a decrease and subsequent increase by the same percentage. The true change is a decrease, with the final cost being slightly lower than the original.

Step-by-step explanation:

The statement is false. If tuition falls by 14% and then rises by 14%, the cost of tuition does not return to the original amount. This is because the 14% increase is applied to the reduced tuition cost, which results in a smaller numerical increase than the initial decrease.

For example, let's say the original tuition is $1,000. A 14% decrease would reduce the tuition by $140, making the new tuition cost $860. A 14% increase on the reduced tuition ($860) would then be $120.40, for a new tuition of $980.40, which is less than the original tuition by $19.60.

The true change in tuition, in this case, would be a decrease of 1.96%, which demonstrates that percent changes are not commutative.