Question

1.
a.)In a two-digit number, the units digit is twice the tens digit. If the number is doubled, it will be 12 more than the reversed number. Find the number.
b.)Eight times the sum of the digits of a certain two-digit number exceeds this number by 19. The tens digit is two less than the units digit. Find the number.
c.)In a two-digit number, the units digit is twice the tens digit. If the number is doubled, it will be 9 more than the number reversed. Find the number.
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Answer 1

x: the unit digit
y: the tens digit

The unit digit is twice the tens digit so:
x=2y

The two digit number:
10y+x

The two digit number doubled:
2(10y+x)

The reversed number:
10x+y

So:
2(10y+x)=10x+y+12

substitute x for 2y

2(10y+2y)=10(2y)+y+12

24y=21y + 12

3y=12
y=4

x=2y=2*4=8

So the number is 48.

Answer 2

xy is the number


a.
unit digit is y
tens is x
units is twice tens digit
y=2x
if it is doubled, it will be 12 more than reversed
20x+2y=12+10y+x
20x+4x=12+20x+x
3x=12
x=4
y=2x
y=2(4)
y=8
48 is the number




b. 8 times sum of digis is bigger than that number by 19
8(x+y)=19+10x+y
x=y-2

8(y-2+y)=19+10(y-2)+y
16y-16=19+10-20+y
y=3
x=y-2
x=3-2
x=1
the number is 13


c.
y=2x
2(10x+y)=9+10y+x
2(10x+2x)=9+20x+x
x=3
y=2x
y=3(3)
y=6

the number is 36



a. 48
b. 13
c. 36