The tens digit of a two-digit number is five less than the ones digit. the sum of four times the tens digit and one-third the ones digit is 19. find the
number and show your work

To find the tens digit, we'll give it the value x...

x = one's digit - 5    Let's call the one's digit y
x = y - 5

Now  lets find the other equation given...

Since the tens digit (x) is y - 5 then

4(y - 5) + 1/3y = 19
4y - 20 + 1/3y = 19
4y + 1/3y = 19 + 20
13/3 y = 39
y = 39 (3/13)
y = 117/13 = 9

So since y (the one's digit)= 9, now substitute it back into the original equation to find the tens digit.

x = y - 5
x = 9 - 5 = 4

Tens digit is 4, ones digit is 9

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