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2 years ago

15

the sum of three consecutive integers is three times the second integer. show that this is true for the three consecutive intege

rs 7,8 and 9

1 answer:

sdas [7]2 years ago

3 0

Step-by-step explanation:

7+8+9=24

second integer is 8 so 8*3=24

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You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and tw

VashaNatasha [74]

Answer: Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

Step-by-step explanation:

Let x= cost per pair of jeans

y = Cost per pair of shorts

z= cost per shirt.

For you, total cost = x+4y+2z= 84

For your friend, total cost = 2x+y+3z=76

For cousin, total cost = x+2y+z= 52

Required system:

$x+4y+2z=84\ (i)\\ 2x+y+3z=76\ (ii)\\ x+2y+z=52\ (iii)$

from (i), $x=84-4y-2z$ (*)

put this in (ii) and (iii) we get

$2\left(84-4y-2z\right)+y+3z=76\\\Rightarrow\ -7y-z+168=76\ (iv)\\\\ 84-4y-2z+2y+z=52\\\Rightarrow\ -2y-z+84=52 \ (v)$

from (iv), $y=-\frac{z-92}{7}\ (vi)$

$\mathrm{Subsititute\:}y=-\frac{z-92}{7}\ \text{in}\ (v)$

$-2\left(-\frac{z-92}{7}\right)-z+84=52\\\\\Rightarrow\ -2\left(-\frac{z-92}{7}\right)-z=-32\\\\\Rightarrow\ -\frac{5z}{7}-\frac{184}{7}=-32\\\\\Rightarrow\ -5z-184=-224\\\\\Rightarrow\ -5z=-40\\\\\Rightarrow\ z=8$

$\mathrm{Subsititute\:}z=8\text{ in (vi)}$

$y=-\frac{8-92}{7}\\\\\Rightarrow \ y=12$

$\mathrm{Subsititute\:}z=8,\:y=12\text{ in (*)}$

$x=84-4\cdot \:12-2\cdot \:8\\\\\Rightarrow\ x= 20$

Hence, x= 20, y= 12 , z=8

So, Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

7 0

2 years ago

How do I say this number 51,634,703,001

olasank [31]

Fifty one billion six hundred thirty four million seven hundred three thousand and one

6 0

2 years ago

Mr. and Mrs. Garcia took their three children to see a matinee on Saturday . They spent a total of $55.50,1 which included $29.2

zmey [24]

N= number of tickets purchased= 5 people went to the movies
t= cost of each ticket

$55.50 - $29.25= n * t
$55.50 - $29.25= 5t
OR
$55.50= 5t + $29.25

ANSWER: $55.50 - $29.25= 5t OR
$55.50= 5t + $29.25 (there were no equations to choose from, but it should look something like one of these).

Hope this helps! :)

7 0

2 years ago

The price of an athletic sweatshirt that normally cost $55 goes on sale for 25% off. What is the new selling price of the sweats

Nata [24]

Answer:

Original price: $ 55

Discount percentage: 25 %

Discount: $13.75

Final Price: $41.25

7 0

2 years ago

When you solve a square root problem, can you just divide it by 2? for example in this picture can you do 25 divided by 2?

user100 [1]

Answer:

No

Step-by-step explanation:

When you square a number, you chose a number and multiplying itself. If you did the square root of 25, you would get 5. However if you divided 25 by 2, you would get 12.5 which is NOT the square root.

7 0

3 years ago

Read 2 more answers