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the water park is a popular field trip destination. falls high filled 2 vans and 9 buses with 383 students. rainy high filled 8 vans and 3 buses with 179 students. find the number of students in each and each bus

Jun 17, 2019

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the water park is a popular field trip destination. falls high filled 2 vans and 9 buses with 383 students.

rainy high filled 8 vans and 3 buses with 179 students. find the number of students in each van and each bus

$$\text{Let \mathbf{v} = students in a \mathbf{\text{van} } } \\ \text{Let \mathbf{b} = students in a \mathbf{\text{bus} } }$$

$$\begin{array}{|lrcll|} \hline \text{rainy high}: & 8v + 3b &=& 179 \quad | \quad \cdot 3 \\ & 24v + 9b &=& 537 \quad (1) \\\\ \text{falls high}: & 2v + 9b &=& 383 \quad (2) \\ \hline (1)-(2): & 24v + 9b - ( 2v + 9b ) &=& 537 - 383 \\ & 24v + 9b - 2v + 9b &=& 154 \\ & 22v &=& 154 \\ & v &=& \frac{154}{22} \\ & \mathbf{ v } &=& \mathbf{7} \\\\ & 2v + 9b &=& 383 \\ & 2\cdot 7 + 9b &=& 383 \\ & 14+ 9b &=& 383 \\ & 9b &=& 369 \\ & b &=& \frac{369}{9} \\ & \mathbf{ b } &=& \mathbf{41} \\ \hline \end{array}$$

In each van are 7 students.
In each bus are 41 students.

Jun 17, 2019