SAT Mathematics Practice Test 7

If Mosteller’s and Current’s formulas give the same estimate for A, then the right-hand sides of these two equations are equal; that is $\frac{\sqrt{\text{hw}}}{60} = \frac{4 + w}{30}$. Multiplying each side of this equation by 60 to isolate the expression $\sqrt{\text{hw}}$ gives $\sqrt{\text{hw}} = 60\left(\frac{4 + w}{30}\right)$ or $\sqrt{\text{hw}} = 2(4 + w)$. Therefore, if Mosteller’s and Current’s formulas give the same estimate for A, then $\sqrt{\text{hw}}$ is equivalent to 2(4 + w).An alternate approach is to multiply the numerator and denominator of Current’s formula by 2, which gives $\frac{2(4 + w)}{60}$. Since it is given that Mosteller’s and Current’s formulas give the same estimate for A, $\frac{2(4 + w)}{60} = \frac{\sqrt{\text{hw}}}{60}$. Therefore, $\sqrt{\text{hw}} = 2(4 + w)$