Question

the following pair of equations indicate means by which the portion divider can be calculated, where as purchased unit size ($ap_u$) is divided by as served portion unit size ($as_u$), which is in turn multiplied against yield ($y$). evaluate the equations and determine their relationship in final values.
$ap_u = 16$
$as_u = 12$
$y =.59$
formula a = $\frac{ap_u}{as_u}\cdot y =$
formula b = $y\cdot\frac{ap_u}{as_u} =$
review the linked section of the prealgebra textbook for problem help
formula a results in a value equal to formula b.
formula a results in a value less than formula b.
formula a results in a value greater than formula b.

Explanation:

Step1: Calculate Formula A

Substitute \(AP_{u} = 16\), \(AS_{u}=12\), \(Y = 0.59\) into Formula A: \(\frac{AP_{u}}{AS_{u}}\cdot Y=\frac{16}{12}\times0.59\).
First, \(\frac{16}{12}=\frac{4}{3}\approx1.333\). Then \(1.333\times0.59 = 0.78647\).

Step2: Calculate Formula B

Substitute \(AP_{u} = 16\), \(AS_{u}=12\), \(Y = 0.59\) into Formula B: \(Y\cdot\frac{AP_{u}}{AS_{u}}=0.59\times\frac{16}{12}\).
Since multiplication is commutative (\(a\times b=b\times a\)), \(0.59\times\frac{16}{12}=\frac{16}{12}\times0.59\).

Answer:

Formula A results in a value equal to Formula B.