Saul works two part-time jobs. Last week, he worked 15 hours at a shoe store, and 21 hours as a telemarketer. His total pay was $289.50. The week before, he made $356.00 for 20 hours at the shoe store and 24 hours telemarketing. Find his hourly wage for each job.
+26382 Saul works two part-time jobs. Last week, he worked 15 hours at a shoe store, and 21 hours as a telemarketer. His total pay was $289.50. The week before, he made $356.00 for 20 hours at the shoe store and 24 hours telemarketing. Find his hourly wage for each job.
hourly wage in shoe store \(=w_s\)
hourly wage in telemarket \(=w_t\)
\(\small{ \begin{array}{lrcll} (1) & 20\ h \cdot w_s + 24\ h \cdot w_t &=& $\ 356.00 \quad & | \quad : 4\\ & 5 \ h \cdot w_s + 6 \ h \cdot w_t &=& $\ 89.00 \\ (2) & 15\ h \cdot w_s + 21\ h \cdot w_t &=& $\ 289.50 \quad & | \quad :3 \\ & 5\ h \cdot w_s + 7\ h \cdot w_t &=& $\ 96.50 \\ \hline \\ (2)-(1): & 5\ h \cdot w_s + 7\ h \cdot w_t - 5 \ h \cdot w_s - 6 \ h \cdot w_t&=& $\ 96.50 - $\ 89.00\\ & 5\ h \cdot w_s- 5 \ h \cdot w_s + 7\ h \cdot w_t - 6 \ h \cdot w_t&=& $\ 96.50 - $\ 89.00\\ & 7\ h \cdot w_t - 6 \ h \cdot w_t&=& $\ 96.50 - $\ 89.00\\ & 1\ h \cdot w_t &=& $\ 7.50\\ & \mathbf{w_t} &\mathbf{=}& \mathbf{ \frac{$\ 7.50} { 1\ h } }\\ \hline \\ & 5 \ h \cdot w_s + 6 \ h \cdot w_t &=& $\ 89.00 \quad & | \quad w_t = \frac{$\ 7.50} { 1\ h }\\ & 5 \ h \cdot w_s + 6 \ h \cdot ( \frac{$\ 7.50} { 1\ h }) &=& $\ 89.00 \\ & 5 \ h \cdot w_s + $\ 45.00 &=& $\ 89.00 \quad & | \quad -$\ 45.00\\ & 5 \ h \cdot w_s &=& $\ 89.00 -$\ 45.00\\ & 5 \ h \cdot w_s &=& $\ 44.00 \quad & | \quad : 5\ h\\ & w_s &=& \frac{ $\ 44.00 } { 5\ h } \\ & \mathbf{w_s} &\mathbf{=}& \mathbf{\frac{$\ 8.80} { 1\ h }} \\ \end{array} }\)
