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GarryVolchara [31]

2 years ago

11

Students are selling pies for a school fundraiser. Customers can buy cherry pies and apple pies. Jennifer sold 12 cherry pies an

d 3 apple pies for a total of 144. Jacob sold 2 cherry pies and 9 apple pies for a total for 126

1 answer:

Tpy6a [65]2 years ago

7 0

Answer: A cherry pie costs 9 and an apple pie cost 12

Step-by-step explanation:

Let an apple pie be represented by a

Let an cherry pie be represented by c

Jennifer sold 12 cherry pies and 3 apple pies for a total of 144. This can be written as:

12c + 3a= 144

Jacob sold 2 cherry pies and 9 apple pies for a total for 126. This can be written as:

2c + 9a = 126

12c + 3a= 144 ............. i

2c + 9a = 126 ........... ii

Multiply equation i by 2

Multiply equation ii by 12

24c + 6a = 288 ........ iii

24c + 108a = 1512 ...... iv

Subtract iv from iii

-102a = -1224

a = 1224/102

a = 12

An apple pie costs 12

From equation i

12c + 3a= 144

12c + (3×12) = 144

12c + 36 = 144

12c = 144 - 36

12c = 108

c = 108/12

c = 9

A cherry pie costs 9

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Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1

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Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

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$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

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Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

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Answer:

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Step-by-step explanation:

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So, the area of this rectangular paper will be

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