SOLUTION: The sum of two numbers is twenty- one. Three times the smaller number is two less than twice the larger number. Find the two numbers.
Student Response
A. 8 and 13
B. 7
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Question 274839: The sum of two numbers is twenty- one. Three times the smaller number is two less than twice the larger number. Find the two numbers.
Student Response
A. 8 and 13
B. 7 and 14
C. 6 and 15
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Let X & Y be the 2 numbers.
X+Y=21 subtract y from both sides.
X=21-Y
-----------------
3 times the smaller (X)= twice the larger (2Y) less 2 (-2)
3X=2Y-2
Replace X with (21-y) in the second equation & solve for y.
3(21-y)=2y-2 expand the left side terms by multiplying by 3.
63-3y=2y-2 subtract -2y & -63 from both sides.
-3y-2y=-2-63 combine like terms.
-5y=-65 divide both sides by -5
y=-65/-5 again divide.
y=13 ans.
x=21-13=8 ans.
Proof:
Numbers are 13 & 8.
replace x with 8 & y with 13.
3*8=2*13-2
24=26-2
24=24
Answer A) is correct.
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