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. ALL DUE IN 7 MIN! HELP NOW OR NEVER

Answer 1

x=the units digit
y=the tens digit.
The number is: 10y + x
The reversed number is: 10x+y
The units digit is twice the tens digit, then: x=2y
a)we suggest this system of equations:

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

We can solve this system of equations by substitution method:
2(10y+2y)=12+[10(2y)+y]
2(12y)=12+21y
24y=12+21y
24y-21y=12
3y=12
y=12/3
y=4

x=2y
x=2(4)=8

The number is: 10y+x=10*4+8=48

Answer: the number is 48. 

b)
the number is: 10x+y
we can suggest this system of equations:

8(x+y)=(10x+y)+19
x=y-2

We can solve this system of equations by substitution method.
8(y-2+y)=[10(y-2)+y]+19
8(2y-2)=11y-20+19
16y-16=11y-1
16y-11y=-1+16
5y=15
y=15/5
y=3

x=y-2
x=3-2=1

The number is: 10x+y=10*1+3=13

Answer:the number is 13.

c)
The number is: 10x+y
The number reversed is: 10y+x
we can suggest this system of equations:

y=2x
2(10x+y)=9+(10y+x)

We solve this system of equations by substitution method:
2(10x+2x)=9+[10(2x)+x]
2(12x)=9+21x
24x=9+21x
24x-21x=9
3x=9
x=9/3
x=3

y=2x
y=2*3=6

The number is: 10x+y=10*3+6=36

Answer: the number is 36