SAT Mathematics Practice Test 7

Questions 39 and 40 refer to the following information.

Mosteller’s formula: A =

√{{\text "hw"}/60}

Current’s formula: A =

{4 + w}/{60}

The formulas above are used in medicine to estimate the body surface area A, in square meters, of infants and children whose weight w ranges between 3 and 30 kilograms and whose height h is measured in centimeters.

Question : 40 of 59

Marks: +1, -0

If Mosteller’s and Current’s formulas give the same estimate for A, which of the following expressions is equivalent to

√\text "hw"

${4 + w}/2$
${4 + w}/{1,800}$
$2(4 + w)$
$(4 + w)^2/2$

Validate

Solution:

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

{√\text "hw"}/60 = {4 + w}/ 30

. Multiplying each side of this equation by 60 to isolate the expression

√\text "hw"

gives

√\text "hw" = 60({4 + w}/30)

√\text "hw" = 2(4 + w)

. Therefore, if Mosteller’s and Current’s formulas give the same estimate for A, then

√\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

{2(4 + w)}/60

. Since it is given that Mosteller’s and Current’s formulas give the same estimate for A,

{2(4 + w)}/60 = {√\text "hw"}/60

. Therefore,

√\text "hw" = 2(4 + w)

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