In triangle ABC, the point D lies on side BC so that BD : DC = 2 : 5. The area of triangle ABD is 24 square units. What is the area of triangle ABC?

Triangles ABD and ADC share the same height from A to line BC, so their areas are in the ratio of their bases, 2 : 5. The whole triangle is therefore 7 parts while ABD is 2 parts, so area ABC = $24\times 7/2=84$ square units. (60 square units is the area of ADC alone, not of the whole triangle.)