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If Benton spent 75% as much as Connie, then did Connie spend 125% as much as Benton?

Use a structured math drawing to explain why the answer to this question is no, and find what percentage of Benton’s ticket price was spent by Connie.

Answer :

Final answer:

Connie did not spend 125% as much as Benton; she spent 133.33% as much. This is because 75% of Connie's spending equates to Benton's full spending, and the inverse calculation shows that Benton's spending is only a portion of Connie's total spending.

Explanation:

If Benton spent 75% as much as Connie, it does not mean that Connie spent 125% as much as Benton. To illustrate this, let's assume Benton spent $75. If this is 75% of what Connie spent, we can set up an equation where 0.75C = $75, solving for C (Connie's spending), we find that C = $75 / 0.75 = $100. Therefore, Connie spent 100% of her amount, which is 33.33% more than Benton's spending, not 125% more.

Calculating Connie's spending as a percentage of Benton's

Now, to find out what percentage of Benton's price was spent by Connie, we need to compare Benton's spending to Connie's. Using Benton's spending as the reference (100%), we relate Connie's $100 to Benton's $75. So we calculate $100 / $75 = 1.333, which means Connie spent 133.33% of what Benton spent, not 125%.

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