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