SOLUTION: #1 Find two consecutive odd integers such that 5 times the first integer is 12 more than 3 times the second. #2 An airplane covered 13 miles of its route while decreasing i

Question 91669: #1 Find two consecutive odd integers such that 5 times the first integer is 12 more than 3 times the second.

#2 An airplane covered 13 miles of its route while decreasing its altitude by 44,000 feet. Find the slope of the airplane's line of descent. Round to the nearest hundredth. [Hint: 1 mi = 5280 feet.]

#3 The difference of two positive numbers is 39. The larger number is 9 less than 4 times the smaller number. What are the two numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
#1 Find two consecutive odd integers
x, (x+2)
such that 5 times the first integer is 12 more than 3 times the second.
5x = 3(x+2) + 12
5x = 3x + 6 + 12
5x - 3x = 18
2x = 18
x = 18/2
x = 9 and 11 are two odd consecutive integers.
:
Check solution
5(9) = 3(11) + 12
45 = 33 + 12
:
:
#2 An airplane covered 13 miles of its route while decreasing its altitude by 44,000 feet. Find the slope of the airplane's line of descent. Round to the nearest hundredth. [Hint: 1 mi = 5280 feet.]
:
One of the definitions of slope is "rise over run", a decrease in altitude would
be a negative rise, so we have altitude change/horizontal change.
:
Change feet to miles: = 8.33 mi
:
Slope = = -.64
:
You could do it with feet too,
Slope = = -.64
:
:
#3 The difference of two positive numbers is 39.
x - y = 39
or
-y = 39 - x
or
+y = (x - 39); use for substitution
:
The larger number is 9 less than 4 times the smaller number.
x = 4y - 9
:
What are the two numbers?
Substitute (x-39) for y in the above equation:
4(x-39) - 9 = x
4x - 156 -9 = x
4x - 165 = x
4x - x = +165
3x = 165
x = 165/3
x = 55
:
Find y: y = 55-39 = 16
:
:
Check solution in x = 4y - 9
55 = 4(16) - 9
55 = 64 - 9
:
:
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