BTGmoderatorDC wrote:The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to m% of stall's revenue and accounted for n% of sales of juice tetra packs. Which of the following expresses m in terms of n?
(A) 100n/(150 - n)
(B) 200n/(250-n)
(C) 200n/(300-n)
(D) 250n/(400-n)
(E) 300n/(500-n)
Source: Princeton Review
$${\text{Particular}}\,\,{\text{case}}\,\,:\,\,n = 100\,\,\, \Rightarrow \,\,\,{\text{only}}\,\,A\,\,{\text{sold}}\,\,\,\, \Rightarrow m = 100\,\,\,\left( {{\text{target}}\,\,{\text{value}}} \right)$$
$$\left( A \right)\,\,\frac{{100 \cdot 100}}{{150 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$\left( B \right)\,\,\frac{{200 \cdot 100}}{{250 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$\left( C \right)\,\,\frac{{200 \cdot 100}}{{300 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{Yes}}!\,\,\,\, \Rightarrow \,\,\,\,{\text{survivor}}!$$
$$\left( D \right)\,\,\frac{{250 \cdot 100}}{{400 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$\left( E \right)\,\,\frac{{300 \cdot 100}}{{500 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$?\,\,:\,\,\left( C \right)\,\,\,,\,\,\,{\text{only}}\,\,{\text{survivor}}$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
