16Hit1600
AlgebraVery hardModel two-rate total with one linear equation

Algebra practice question

A glaciologist analyzes an ice core that is 1,200 centimeters long and represents exactly 700 years of snowfall. In the upper section of the core, each year of snowfall is represented by a layer 3 centimeters thick. In the lower section, compression has reduced each year of snowfall to a layer 1.2 centimeters thick.

How many centimeters long is the upper section of the core?

Answer: 600

Let x be the length, in centimeters, of the upper section; the lower section is 1200 - x centimeters long. The upper section represents x/3 years and the lower section represents (1200 - x)/1.2 years, so x/3 + (1200 - x)/1.2 = 700. Expanding gives x/3 + 1000 - (5/6)x = 700, so -(1/2)x = -300 and x = 600. Check: 600/3 = 200 years and 600/1.2 = 500 years, and 200 + 500 = 700.

Common wrong answers

If you answered 200
That's the number of years the upper section represents, not its length in centimeters — multiply by the 3 cm per year to get 600.
If you answered 360
You found the extra length beyond 700 years of fully compressed snow (1200 - 700(1.2) = 360), but you still need to convert: each upper-section year adds 1.8 cm of extra length, so 360/1.8 = 200 years, which is 600 cm.
If you answered 500
That's the number of years the lower section represents. The question asks for the length in centimeters of the upper section, which covers the other 200 years at 3 cm each.

More Algebra questions

Not affiliated with the College Board. SAT is a trademark of the College Board.