Mathematics, 20.12.2019 04:31, chaseashley24

Alady came to the market to sell eggs. her first customer bought 1/2 of all her eggs and 1/2 of an egg. her second customer bought 1/2 of all the remaining eggs and 1/2 of an egg. finally, a third customer bought 1/2 of all of her remaining eggs and 1 2 of an egg. at this point she had sold all of the eggs she had brought to the market so she went home. how many eggs did the lady have when she first came to the market?

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answered: joel53

total eggs = 7

Step-by-step explanation:

We can start by number of eggs.

Total eggs =

1st buyer

the first buyer buys 1/2 of all eggs and another 1/2

$x-\left(\dfrac{x}{2}+\dfrac{1}{2}\right)$

we can say that the remaining eggs are equal to this above equation and call it .

$A = x-\left(\dfrac{x}{2}+\dfrac{1}{2}\right)$

we can simplify it further

$A = x-\dfrac{x}{2}-\dfrac{1}{2}$

$A = \dfrac{x}{2}-\dfrac{1}{2}$

$A = \dfrac{1}{2}(x-1)$

2nd buyer

the second buyer takes 1/2 of the remaining eggs and another 1/2 egg.

remaining eggs from the first buyer were

remaining eggs from the second buyer are:

$A-\left(\dfrac{A}{2}+\dfrac{1}{2}\right)$

we can call these remaining eggs as .

$B = A-\left(\dfrac{A}{2}+\dfrac{1}{2}\right)$

now simplify (similar to how equation was simplified)

$B = \dfrac{1}{2}(A-1)$

we can further simplify it by substituting the equation , making equation in terms of

$B = \dfrac{1}{2}\left(\dfrac{x-1}{2} - 1\right)$

$B = \dfrac{x}{4} -\dfrac{1}{4} - \dfrac{1}{2}$

$B = \dfrac{x}{4} -\dfrac{3}{4}$

this is the amount of the remaining eggs after the 2nd buyer.

3rd buyer

This is where things get interesting. The third buyer takes half of what remaining, i.e .

$B-\left(\dfrac{B}{2}+\dfrac{1}{2}\right)$

but this time, there are no remaining eggs!

So the equation is equal to zero!

$0 = B-\left(\dfrac{B}{2}+\dfrac{1}{2}\right)$

simplify (as we were doing for previous equations)

$\dfrac{1}{2}(B-1) = 0$

now we can substitute the equation of

$\dfrac{1}{2}\left(\dfrac{x}{4} -\dfrac{3}{4}-1\right) = 0$

all we need to do now is just solve for x!

$0 = \dfrac{x}{4} -\dfrac{3}{4}-1$

$\dfrac{x}{4} -\dfrac{3}{4} = 1$

x-3 = 4

x = 7

The total number of eggs when the lady first came to the market were 7!

Hope this helps! :)

answered: Guest

As you know john locke said he wanted life liberty and the pursuit of happiness so thomas jefferson was inspired about what john locke said so thomas jefferson wrote the declaration of independence for people to be free for people to be happy

answered: Guest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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Alady came to the market to sell eggs. her first customer bought 1/2 of all her eggs and 1/2 of an e...