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Question 532047: 1) Two numbers are in the ratio of 3:5. If 8 is subtracted from their sum, the result is 40. What is the larger number?
2)The ratio of two complementary angles is 2:7. What are the measures of the two angles?
3) Two angles are supplementary. The larger angles is 3 less than twice the smaller angle. Find the measure of the larger angle.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 1) Two numbers are in the ratio of 3:5. If 8 is subtracted from their sum, the result is 40.
What is the larger number?
Let x = the multiplier
then
3x = the smaller number
5x = the larger
"If 8 is subtracted from their sum, the result is 40."
5x + 3x - 8 = 40
8x = 40 + 8
8x = 48
x = 48/8
x = 6 is the multiplier
therefore
6(5) = 30 is the larger number
and
6(3) = 18 is the smaller, check this in the given statement
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2)The ratio of two complementary angles is 2:7. What are the measures of the two angles?
let x = the multiplier
2x + 7x = 90
9x = 90
x = 10 is the multiplier
then
20 and 70 are the two angles
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3) Two angles are supplementary. The larger angles is 3 less than twice the smaller angle. Find the measure of the larger angle.
let a = the larger angle
let b = the smaller
a = 2b-3
:
a + b = 180
2b-3 + b = 180
3b - 3 = 180
3b = 180 + 3
3b = 138
b = 183/3
b = 61
Find a
a = 2(61) - 3
a = 122 - 3
a = 119 degrees is the larger angle
:
Check this 119 + 61 = 180
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