Question

1.

Answer 1

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

Answer 2

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.