SOLUTION: Twice the small number is 5 more than 2/3 the larger number. Three times the larger number is 4 less than 15 times the smaller number. Find the value of both numbers.
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Question 358073: Twice the small number is 5 more than 2/3 the larger number. Three times the larger number is 4 less than 15 times the smaller number. Find the value of both numbers. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Let x = the large number
Let y = the small number
:
Write an equation for each statement:
:
Twice the small number is 5 more than 2/3 the larger number.
2y = x + 5
Get rid of that annoying fraction, multiply by 3, results:
6y = 2x + 15
-2x + 6y = 15
:
Three times the larger number is 4 less than 15 times the smaller number.
3x = 15y - 4
3x - 15y = -4
:
Use elimination here, multiply the 1st equation by 3, and the 2nd equation by 2
-6x + 18y = 45
+6x - 20y = -8
-------------------adding eliminates x, find y
-12y = 37
y =
:
Use the 1st equation to find x
-2x + 6() = 15
-2x + ) = 15
Multiply by 2
-4x - 37 = 30
-4x = 30 + 37
-4x = 67
x =
:
A couple nasty fractions, see if they work in the 2nd equation
3x - 15y = -4
Substitute
3() - 15( = -4 + ( = -4
multiply by 12 to get rid of those annoying fractions
3(201) + 555 = -48
-603 + 555 = -48; it does work, amazing isn't it!
