Princeton Review
Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?
A. 0.8b
B. 1.1b
C. 1.2b
D. 10b
E. 11b
OA E.
Jake and Ryan worked together on a job for which they were
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Let the hourly wage = $1 per hour.AAPL wrote:Princeton Review
Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?
A. 0.8b
B. 1.1b
C. 1.2b
D. 10b
E. 11b
Let Ryan's time = 10 hours, implying that Jake's time = 10 + (20% of 10) = 10 + 2 = 12 hours.
Thus:
Total number of work hours = 10+12 = 22 hours.
Total pay = (hourly wage)(total number of work hours) = 1*22 = $22.
Since the total pay = 10+12 = $22, and Jake and Ryan each receive the same amount in advance, the amount Jake and Ryan each receive in advance = 22/2 = $11.
Since Ryan works 10 hours at a rate of $1 per hour, Ryan's take-home pay = (hourly wage)(number of work hours) = 1*10 = $10.
Ryan gave Jake b dollars.
Since Ryan receives $11 in advance but takes home only $10, b=1.
In terms of b, how much was Jake paid in advance?
Since Jake and Ryan each receive $11 in advance, the correct answer must yield a value of 11 when b=1.
Only E works:
11b = 11*1 = 11.
The correct answer is E.
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$$\left. \matrix{AAPL wrote:Princeton Review
Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?
A. 0.8b
B. 1.1b
C. 1.2b
D. 10b
E. 11b
{\rm{Ryan}}\,\,\left\{ \matrix{
\,\,5t\,\,\,{\rm{hours}} \hfill \cr
\,\,\$ \,\,\left( {a - b} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{{a - b} \over {5t}}\,\,\,{\$ \over {{\rm{hour}}}} \hfill \cr
{\rm{Jake}}\,\,\,\,\left\{ \matrix{
\,\,5t + {1 \over 5}\left( {5t} \right) = 6t\,\,\,{\rm{hours}} \hfill \cr
\,\,\$ \,\,\left( {a + b} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{{a + b} \over {6t}}\,\,\,{\$ \over {{\rm{hour}}}}\,\,\,\,\,\, \hfill \cr} \right\}\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{stem}}} \,\,\,\,\,\,\,\,{{a - b} \over {5t}} = \,\,\,\,{{a + b} \over {6t}}$$
$$?\,\,:\,\,\,a = f\left( b \right)$$
$${{a - b} \over {5t}} = \,\,\,\,{{a + b} \over {6t}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,6\left( {a - b} \right) = 5\left( {a + b} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,?\,\,\,:\,\,\,a = 11b$$
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
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We can assume each was given 110 dollars for the job. Furthermore, we can assume that Ryan worked 10 hours and Jake worked 12 hours. Thus, the hourly wage, which must be equal for both, should be:AAPL wrote:Princeton Review
Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?
A. 0.8b
B. 1.1b
C. 1.2b
D. 10b
E. 11b
OA E.
(110 + 110)/(10 + 12) = 220/22 = $10
Therefore, we see that Ryan should give Jake $10 so that Ryan would have $100 (notice that 10 x $10 = $100) and Jake would have $120 (notice that 12 x $10 = $120).
We see that a = 110 and b = 10, so a = 11b.
Answer: E
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