Assume that the cost for one person was not over $250.
See solution.
Practice makes perfect
Let's highlight the hypothesis and the conclusion in the statement we are asked to prove.
If the cost of a cruise for two person is over$500,
then the cost for one person is more than$250.
Let's introduce variable x for the cost of the cruise for one person.
Using this variable, we can rewrite the claim.
If 2x>500,
then x>250.
We are asked to use an indirect argument to prove this claim.
Step 1
We start the indirect proof by assuming that the conclusion is not true.
Assumption: x≯ 250
This means that we assume that x is less than or equal to 250.
Step 2
In the next step of an indirect proof we investigate consequences of our assumption until we find something that contradicts the hypothesis of the original statement.
Let's look at the consequences of x≤ 250, keeping in mind that the original hypothesis is an inequality involving 2x.
Since our assumption x≤ 250 contradicts 2x>500, our assumption must be false.
This proves the given conditional statement.
If 2x>500,
then x>250.
If Tavia and her friend paid over $500 for the cruise, then the cost of the cruise for a person is more than $250.
