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Sedaia [141]
3 years ago
9

a ski chalet offers 2 weekend packages. one package provides 2 nights and 3 meals for$280. the other provides 2 nights and 5 mea

ls for $320. write and solve a system of equations to find the cost per night and per meal.
Mathematics
1 answer:
Helga [31]3 years ago
8 0


<span> <span>1st</span></span><span> formula 2n + 3m = 280
</span><span><span>
</span><span>2nd</span></span><span> formula 2n + 5m = 320
</span><span><span>
</span><span>rearrange 1st</span> formula to equal n:</span>

    <span><span>2n = -3m + 280
</span>      </span><span>n = -3/2 m + 140
</span><span><span>
</span><span>rearrange 2nd</span> formula to equal n:</span>

 <span><span>2n = -5m + 320
</span> </span><span>n = -5/2m + 160
</span><span><span> so now you have

</span>-3/2m + 140 = -5/2m + 160 </span>

<span><span>Rearrange to become:
</span> </span><span><span>-3/2m + 5/2m = 160 - 140
</span> </span><span>m = 20
</span><span>
</span>

<span>Now place 20 into the very 1st</span><span><span> equation in place of the letter m
</span> </span><span><span>2n + 3(20) = 280
</span> </span><span><span>2n + 60 = 280
</span> </span><span><span>2n = 220
</span> </span><span>n = 110
</span><span><span>
</span>so it costs $110 per night, $20 per meal</span>


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