The measure of the supplement of an angle exceeds three times the measure of the complement of the angle by 12. Find the measure of half of the supplement.

  64.5°

Step-by-step explanation:

The supplement of angle x is 180-x. The complement of the same angle is 90-x, which is 90 less than the supplement.

We can let 'a' represent half the measure of the supplement. Then 2a is the measure of the supplement, and we are given the relation ...

  2a -(3(2a-90)) = 12

  2a -6a +270 = 12 . . . simplify

  258 = 4a . . . . . . . . . . add 4a-12

  a = 64.5

The measure of half the supplement is 64.5 degrees.

Additional comment

Then the supplement of the angle is 129°, and the angle is 51°. Its complement is 39°. 3 times the complement is 117°, which is 12° less than the supplement, as required.

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There are many ways to assign the variable(s) in this problem. Here, we chose one that is pretty direct: the value of the variable answers the question. If you let the variable represent the angle, its complement, or its supplement, then additional work is required to answer the question after the value of the variable is found.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!