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Katyanochek1 [597]

3 years ago

12

Scarlett works as a salesperson at an electronics store and sells phones and phone accessories. Scarlett earns a $14 commission

for every phone she sells and a $3 commission for every accessory she sells. On a given day, Scarlett made a total of $344 in commission from selling a total of 45 phones and accessories. Determine the number of phones sold and the number of accessories sold.

1 answer:

Natasha2012 [34]3 years ago

4 0

Answer:

19 phones and 26 accessories

Step-by-step explanation:

What we need here is to work with a two-equation system, where one equation corresponds to income and the other to the amounts sold.

First, lets think on the amounts. She sold a p amount of phones and an a amount of accessories, such that in total she sold 45 items. So:

a + p = 45 [equation 1]

Then, she made a total money of $344, for selling this 45 items. With prices of $3 for accessories and $14 for phones. The equation is:

3a + 14 p = 344 [equation 2]

If we take equation 1 en get the value of a, by subtracting p en both sides:

a + p - p = 45 - p

a = 45 - p [equation 1']

If we pick this last equation and replace in equation 2 we have:

3a + 14 p = 344

3 (45-p) + 14p = 344

135 - 3p + 14p = 344

135 + 11 p = 344

Subtracting 135 in both sides:

135 -135 + 11p = 344 - 135

11p = 209

Dividing by 11 in both sides:

11p/11 = 209/11

p = 19

So, Scarlett sold 19 phones. If we replace it in equation 1:

a + 19 = 45

Subtracting 19 in both sides:

a = 26

She also sold 26 accessories.

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Part A) $y=\frac{3}{4}x-\frac{1}{4}$

Part B) $y=\frac{2}{7}x-\frac{5}{7}$

Part C) $y=\frac{2}{7}x+\frac{8}{7}$

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the median from N

we Know that

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step 1

Find the midpoint segment LP

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L(-3, 6) and P(1, -8)

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step 2

Find the slope of the segment NM

The formula to calculate the slope between two points is equal to

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we have

N(3, 2) and M(-1,-1)

substitute the values

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$m=\frac{3}{4}$

step 3

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{3}{4}$

$point\ N(3, 2)$

substitute

$y-2=\frac{3}{4}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{3}{4}x-\frac{9}{4}$

$y=\frac{3}{4}x-\frac{9}{4}+2$

$y=\frac{3}{4}x-\frac{1}{4}$

Part B) Find the equation of the right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 3

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

so

$m_2=\frac{2}{7}$

step 4

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{7}$

$point\ M(-1,-1)$ ----> midpoint LP

substitute

$y+1=\frac{2}{7}(x+1)$

step 5

Convert to slope intercept form

Isolate the variable y

$y+1=\frac{2}{7}x+\frac{2}{7}$

$y=\frac{2}{7}x+\frac{2}{7}-1$

$y=\frac{2}{7}x-\frac{5}{7}$

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 2

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

so

$m_2=\frac{2}{7}$

step 3

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{7}$

$point\ N(3,2)$

substitute

$y-2=\frac{2}{7}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{2}{7}x-\frac{6}{7}$

$y=\frac{2}{7}x-\frac{6}{7}+2$

$y=\frac{2}{7}x+\frac{8}{7}$

7 0

3 years ago