Find the angle.

Find the measure of an angle if the measure of the angle 
is  8 degrees less than three times the measure of its supplement. 

x = the angle
180 - x = supplement {supplementary angles add up to 180}

x = 3(180 - x) - 8 {measure of angle is 8 less than 3x supplement}
x = 540 - 3x - 8 {used distributive property}
x = 532 - 3x {combined like terms}
4x = 532 {added 3x to both sides}
x = 133 {divided both sides by 4}

133 is the angle

© Algebra House

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Find the number.

Twice a number is 32 less than 4 times the number.
Find the number.
  
x = the number

2x = 4x - 32 {twice a number is 32 less than 4 times the number}
-2x = -32 {subtracted 4x from both sides}
x = 16 {divided both sides by -2}

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Number Problem

Four times a number added to another number is 36.  Three times the first number minus the other number is 20. Find the numbers.

x = the number
y = other number 

4x + y = 36 {four times a number added to another number is 36}
3x - y = 20 {three times the 1st minus other is 20}
-------------
7x = 56 {added the two equations together and eliminated the y}
x = 8 {divided both sides by 7}
The first number is 8. 

4x + y = 36 {top equation}
4(8) + y = 36 {substituted 8 in for x}
32 + y = 36 {multiplied 4 by 8}
y = 4 {subtracted 32 from both sides}
The other number is 4. 
 
The two numbers are 8 and 4 

© Algebra House

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Find the missing score.

A student having marks of 65 and 75 wishes to raise the average of the two marks and a test mark to 80. What must he receive on the test?

Add the two given scores with the missing score,
divide by 3, and that is the average.
Assuming, everything is weighted the same. 


65 + 75 + x
---------------  =  80 
         3 


140 + x
-----------  =  80 {combined like terms in numerator}
   3 


140 + x = 240 {multiplied both sides by 3}

x = 100 {subtracted 140 from both sides} 

He must receive 100% on the test. 

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