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4 years ago

9

Leonard uses 3 peach slices and 1 banana for his fruit parfaits. If he used 42 peach slices to make parfaits for his friends, ho

w many bananas did he use?

2 answers:

Fiesta28 [93]4 years ago

6 0

He used 14 bananas for his parfait.

Yanka [14]4 years ago

4 0

Answer:

14

Step-by-step explanation:

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<em>LCM</em> = $8y^{4}(y+ 10)^{2}(y + 8)$

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Taking $8y^{4}$ common:

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Using <em>factorization</em> method:

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Taking $2y^{2}$ common:

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Using <em>factorization</em> method:

$\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10) ............ (2)$

The underlined parts show the Highest Common Factor(HCF).

i.e. <em>HCF</em> is $2y^{2} (y+ 10)$ .

We know the relation between <em>LCM, HCF</em> of the two numbers <em>'p' , 'q'</em> and the <em>numbers</em> themselves as:

$HCF \times LCM = p \times q$

Using equations <em>(1)</em> and <em>(2)</em>: $\Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)$

Hence, <em>LCM</em> = $8y^{4}(y+ 10)^{2}(y + 8)$

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