Is an Elemental Calcium 500mg + Vitamin D3 500IU Tablet suitable for both a 14-year-old and a 47-year-old to take?

Calcium and Vitamin D needs vary quite a bit across age groups, so it's good you're thinking about both separately. This combination can generally suit a growing teenager as well as an adult, but the right dose and duration differ by age, diet and any existing deficiency, and a 14-year-old shouldn't simply take an adult dose without guidance. Check with a pediatrician for the teen and a physician for the adult so each gets a dose that's actually right for them.