Question 53303: The sum of the units digit and 3 times the tens digit of a 2 digit number is 14. The sum of the tens digit and twice the units digit is 18. Find the number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The sum of the units digit and 3 times the tens digit of a 2 digit number is 14. The sum of the tens digit and twice the units digit is 18. Find the number.
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A two digit number; let x = the 10s digit and y = units digit
:
From each sentence write an expression:
:
"sum of the units digit and 3 times the tens digit is 14."
y + 3x = 14
:
"The sum of the tens digit and twice the units digit is 18."
x + 2y = 18
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Two equations, two unknowns:
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Using the first equation:
y + 3x = 14
Rearrange it
y = 14-3x, substitute this for y in the 2nd equation & solve for x:
:
x + 2(14-3x) = 18
x + 28 - 6x = 18
-5x = 18 - 28
x = -10/-5
x = +2
:
y = 14 - 3x
y = 14 - 3(2)
y = 8
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Our number is 28, check it in the original statement:
:
"The sum of the tens digit and twice the units digit is 18."
2 + 2(8) = 18
and
"sum of the units digit and 3 times the tens digit is 14."
8 + 3(2) = 14
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