Problem C

Gone Shopping

While grocery shopping, Terry has a way to approximate the total cost of his purchases. He simply approximates that each item will cost \(\$3.00\).

One day, Terry purchased \(20\) items. He purchased items that each had an actual cost of either \(\$1.00\), \(\$3.00\), or \(\$7.50\). Exactly seven of the purchased items had an actual cost of \(\$3.00\). If the total actual cost of the \(20\) items was the same as the total approximated cost, how many items had an actual cost of \(\$7.50\)?

**Themes:** Algebra, Number Sense