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Alex17521 [72]
3 years ago
11

a recipe requires 3/4 cup of nuts to make 1 cake. what is the maximum number of cakes that can be made using 7 1/2 cups of nuts

Mathematics
1 answer:
ladessa [460]3 years ago
8 0
7.5/.75 = 10
10 cakes
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The picture is the qeustion
alexdok [17]

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n=64

Step-by-step explanation:

Let think algebracially. One of the terms in the set is a fraction. A natural number must be a whole number so this means that

n must be a multiple of 8.

*<em>N</em><em> </em><em>must</em><em> </em><em>be</em><em> </em><em>a</em><em> </em><em>multiple</em><em> </em><em>of</em><em> </em><em>8</em><em>.</em>

<em>Look</em><em> </em><em>at</em><em> </em><em>the</em><em> </em><em>third</em><em> </em><em>term</em><em>,</em><em> </em><em>we</em><em> </em><em>know</em><em> </em><em>that</em><em> </em><em>a</em><em> </em><em>square</em><em> </em><em>root</em><em> </em><em>must</em><em> </em><em>produce</em><em> </em><em>a</em><em> </em><em>perfect</em><em> </em><em>square</em><em> </em><em>term</em><em> </em><em>to</em><em> </em><em>get</em><em> </em><em>a</em><em> </em><em>natural</em><em> </em><em>number</em><em>.</em><em> </em><em>So</em><em> </em><em>n</em><em> </em><em>must</em><em> </em><em>be</em><em> </em><em>a</em><em> </em><em>multiple</em><em> </em><em>of</em><em> </em><em>8</em><em> </em><em>that</em><em> </em><em>makes</em><em> </em><em>the</em><em> </em><em>radical</em><em> </em><em>a</em><em> </em><em>perfect</em><em> </em><em>square</em><em> </em>

<em>Perfect</em><em> </em><em>squares</em><em> </em><em>are</em><em>.</em>

<em>0</em><em>,</em><em>1</em><em>,</em><em>4</em><em>,</em><em>9</em><em>,</em><em>16</em><em>,</em><em>25</em><em>,</em><em>36</em><em>,</em><em>49</em><em>,</em><em>64</em><em>,</em><em>81</em><em>,</em><em>100</em><em>,</em><em>12</em><em>1</em><em>,</em><em>144</em><em>,</em><em>169</em><em>,</em><em>196</em><em>,</em><em>225</em><em>,</em><em> </em><em>256</em><em>,</em><em> </em><em>289</em>

<em>N</em><em> </em><em>has</em><em> </em><em>to</em><em> </em><em>compute</em><em> </em><em>a</em><em> </em><em>sum</em><em> </em><em> </em><em>greater</em><em> </em><em>than</em><em> </em><em>225</em><em> </em><em>so</em><em> </em><em>the</em><em> </em><em>perfect</em><em> </em><em>squares</em><em> </em><em>we</em><em> </em><em>look</em><em> </em><em>at</em><em> </em><em>must</em><em> </em><em>be</em><em> </em><em>greater</em><em> </em><em>than</em><em> </em><em>225</em><em>.</em>

<em>The</em><em> </em><em>next</em><em> </em><em>one</em><em> </em><em>is</em><em> </em><em>256</em><em> </em><em>but</em>

<em>256 - 225 = 31</em>

<em>31 \div 8 =  \frac{31}{8}</em>

<em>which</em><em> </em><em>isn't</em><em> </em><em>rational</em><em> </em><em>so</em><em> </em><em>256</em><em> </em><em>won't</em><em> </em><em>work</em><em>.</em><em> </em><em>Let</em><em> </em><em>try</em><em> </em><em>28</em><em>9</em>

<em>289 - 225 = 64</em>

<em>64  \div 8 = 8</em>

<em>and</em>

<em>33 + 64 = 97</em>

<em>So</em><em> </em><em>64</em><em> </em><em>works</em><em>.</em><em> </em><em>64</em><em> </em><em>is</em><em> </em><em>the</em><em> </em><em>answer</em>

<em>n</em><em>=</em><em>64</em>

6 0
3 years ago
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