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marin [14]
3 years ago
15

A rectangular room is 22 meters longer than it is wide, and its perimeter is 1616 meters. find the dimension of the room.

Mathematics
1 answer:
Eddi Din [679]3 years ago
3 0
W= width; L= length =w+22m; p= perimeter= 2(L+w)
1616 meters= 2 (L+w) substitute for L
1616m+ 2(w+22m+w) divide each side by 2

808m= 2w+22m subtract 22m from each side
786m=2w divide each side by 2
393m=w Anwer: The width is 393 meters
L=w+22m=393m+22m=415m Answer: The length is 415 meters
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  • Yes it's reasonable
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Refer to the diagram below.

The explanation for each part is below as well.

========================================================

Part 1

i = number of individual nail polish bottles

s = number of sets of 4

12i = money earned from just selling the individual bottles only

36s = money earned from just selling the sets of 4 only

12i+36s = total money earned = 300

12i+36s = 300 is the equation to set up

This is the same as 300 = 12i+36s  because A = B is the same as B = A.

========================================================

Part 2

Plug in s = 5 to represent she sold 5 sets. Let's solve for i

12i+36s = 300

12i+36(5) = 300

12i+180 = 300

12i = 300-180

12i = 120

i = 120/12

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If she wants to sell $300 worth of product overall, and she already sold 5 sets so far, then she needs to sell 10 individual bottles to reach this monthly goal.

========================================================

Part 3

Yes it's reasonable to reach this goal. This is because the value of i (from part 2) was some positive whole number.

========================================================

Part 4

We'll repeat part 2 but with s = 12

12i+36s = 300

12i+36(12) = 300

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12i = -132

i = -132/12

i = -11

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The instructions further state that $432 was already made and that she exceeded her goal. Meaning that she doesn't have to worry about selling the individual bottles if selling the sets has her reach something over $300.

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