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3 years ago

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Gracie, Mary, and Nancy each have a small collection of seashells. Gracie has 5 more than times the number of shells Mary has. N

ancy has 1 more than times the number of shells Mary has. Gracie and Nancy have the same number of shells. If x is the number of shells Mary has, identify the equation that represents this situation and identify its solution.

2 answers:

Zielflug [23.3K]3 years ago

4 0

Answer:

3/2 x +1 = 5/4x - 5

3/2 x+1 =5/4

x−5

Step 1: Subtract 5/4x from both sides.

3/2 x+1−5/4

x=5

4x−5−5/4x

1/4x+1=−5

Step 2: Subtract 1 from both sides.

1/4x+1−1=−5−1

1/4

x=−6

Step 3: Multiply both sides by 4.

4*(1/4x)=(4)*(−6)

x=−24 Mary has 24 shells

Answer:

-x=−24

x = 24 shells

Step-by-step explanation:

1. 2 3/4 x 16 = 44 + 6 = 50 shells x= 16

2 3/4 x 24 = 66 + 6 = 72 x = 24

We see the side workings in bold as if Mary has 24 and Nancy has 1x more

Then Nancy 24+24 = 48 where Gracie 5 x 24 = 120 and we have 72-48 = 24 and 120-72 = 48 being the same as Nancy. You can ignore or check the rest in explanation.

2 3/4 x 18 = 49 1/2 + 6 = 55 1/2 x= 18

2. 2 3/4 x 16 = 44 -4 = 40 shells x = 16 2 3/4 x 24 = 66 - 4 = 62 x = 24

2 3/4 x 18 = 49 1/2 - 4 = 45 1/2 x = 18

3. 2 3/4 x 16 = 44 + 4 = 48 shells x = 16 2 3/4 x 24 = 66 + 4 = 70 x = 24

2 3/4 x 18 = 49 1/2 + 4 =53 1/2 x = 18

snow_lady [41]2 years ago

4 0

Answer:

x = 18

Step-by-step explanation:

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Maurinko [17]

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3 years ago

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representa

Aleksandr [31]

Answer:

$y=3.529 x +37.91$

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

$y(8) = 3.529*8 + 37.91= 66.142$

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

$y(11) = 3.529*11 + 37.91= 76.729$

Step-by-step explanation:

For this case we have the following data:

Miles Traveled x: 2,3,10,7,8,15,3,1,11

Sales y :31,33,78,62,65,61,48,55,120

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =60$

$\sum_{i=1}^n y_i =553$

$\sum_{i=1}^n x^2_i =582$

$\sum_{i=1}^n y^2_i =39653$

$\sum_{i=1}^n x_i y_i =4329$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=582-\frac{60^2}{9}=182$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=4329-\frac{60*553}{9}=642.33$

And the slope would be:

$m=\frac{642.33}{182}=3.529$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{60}{9}=6.67$

$\bar y= \frac{\sum y_i}{n}=\frac{553}{9}=61.44$

And we can find the intercept using this:

$b=\bar y -m \bar x=61.44-(3.529*6.67)=37.91$

So the line would be given by:

$y=3.529 x +37.91$

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

$y(8) = 3.529*8 + 37.91= 66.142$

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

$y(11) = 3.529*11 + 37.91= 76.729$

4 0

3 years ago