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.
1 answer:
<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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