Question

Please help with these math problems I will give 50 points if you answer all

Answer 1

Creating and Solving Equations​

Write an equation for each description.​

We will call N the searched number​

1. Eight times the difference of a number and 2 is the same as 3 times the sum of the number and 3.​

8(N-2) = 3(N+3)​

8N - 16 = 3N + 9 ​

8N - 3N = 9 + 16​

5N = 25​

N = 25/5 = 5 ​ ANSWER 1 = 5

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2. The sum of -7 times a number and 8 times the sum of the number and 1 is the same as the number minus 7​

-7N + 8(N+1) = N - 7​

-7N +8N +8 = N -7​

N + 8 = N -7​

ERROR There is no such number​ ANSWER 2 = does no exist.

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3. The quotient of the difference of a number and 24 divided by 8 is the same as the number divided by 6​

(N-24)/8 = N/6​

6(N-24) = 8N​

6N -144 = 8N​

-144 = 8N-6N​

-144= 2N​

N = -144/2 = -72​ ANSWER 3 = -72

We can check it by replacing this number​

(-72-24)/8 = -72/6​

-96/8 = -72/6​

-12 = -12 ¡Checked!​

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4. Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value of $10.90​.

How many dimes and how many quarters does she have? ​[Hint: Use the decimal values of the c coins to write an equation]

We will call d and q to the number of dimes and quarters respectively.​

d + q = 61​ Equation 1

0.10d + 0.25q = $10.90​ multiplying each coin by its value in dollars. Equation 2

d + d+3 = 61 there are three more quarters than dimes​

2d = 61-3 = 58​

d = 58/2 = 29 dimes this is the number of dimes​

q = d+3 = 29+3 = 32 quarters this is the number of quarters​

ANSWER 4 = She has 32 quarters and 29 dimes

​We can check this by replacing the values in Equation 2

29*$0.10 + 32*$0.25 = $2.90 + $8 = $10.90 ¡Checked!​

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5 Penn used the formula for the sum of the angles inside a polygon: ​Sum of the interior angles = (n-2)180, where n is the number of angles of the polygon. Penn's answer is 1,980 degrees. How many angles does the polygon have?

(n -2 )*180º = 1,980º​

180n -360º = 1,980º​

180n = 1,980+360º = 2,340º​

n= 2,340º/180º = 13 This is the number of angles of the polygon.​

ANSWER 5 = 13 angles

$\textit{\textbf{Spymore}}$​​

Answer 2

1. Eight times the difference of a number and 2 is the same as 3 times the sum of the number and 3.​

8(N-2) = 3(N+3)​

8N - 16 = 3N + 9 ​

8N - 3N = 9 + 16​

5N = 25​

N = 25/5 = 5 ​ ANSWER 1 = 5

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2. The sum of -7 times a number and 8 times the sum of the number and 1 is the same as the number minus 7​

-7N + 8(N+1) = N - 7​

-7N +8N +8 = N -7​

N + 8 = N -7​

ERROR There is no such number​ ANSWER 2 = does no exist.

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3. The quotient of the difference of a number and 24 divided by 8 is the same as the number divided by 6​

(N-24)/8 = N/6​

6(N-24) = 8N​

6N -144 = 8N​

-144 = 8N-6N​

-144= 2N​

N = -144/2 = -72​ ANSWER 3 = -72

We can check it by replacing this number​

(-72-24)/8 = -72/6​

-96/8 = -72/6​

-12 = -12 ¡Checked!​

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4. Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value of $10.90​.

How many dimes and how many quarters does she have? ​[Hint: Use the decimal values of the c coins to write an equation]

We will call d and q to the number of dimes and quarters respectively.​

d + q = 61​ Equation 1

0.10d + 0.25q = $10.90​ multiplying each coin by its value in dollars. Equation 2

d + d+3 = 61 there are three more quarters than dimes​

2d = 61-3 = 58​

d = 58/2 = 29 dimes this is the number of dimes​

q = d+3 = 29+3 = 32 quarters this is the number of quarters​

ANSWER 4 = She has 32 quarters and 29 dimes

​We can check this by replacing the values in Equation 2

29*$0.10 + 32*$0.25 = $2.90 + $8 = $10.90 ¡Checked!​

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5 Penn used the formula for the sum of the angles inside a polygon: ​Sum of the interior angles = (n-2)180, where n is the number of angles of the polygon. Penn's answer is 1,980 degrees. How many angles does the polygon have?

(n -2 )*180º = 1,980º​

180n -360º = 1,980º​

180n = 1,980+360º = 2,340º​

n= 2,340º/180º = 13 This is the number of angles of the polygon.​

ANSWER 5 = 13 angles