Question 262876
let x = the 10's digit
let y = the units
then 10x + y = the two digit number
:
Write an equation for each statement:
:
"A certain two-digit number has a value that is 2 more than 6 times the sum of its digits."
10x + y = 6(x + y) + 2
10x + y = 6x + 6y + 2
10x - 6x = 6y - y + 2
4x = 5y + 2
:
" The tens digit is 1 more than the units digit."
x = y + 1
:
Using equation 4x = 5y + 2, replace x with (y+1)
4(y+1) = 5y + 2
4y + 4 = 5y + 2
4 - 2 = 5y - 4y
2 = y
then
x = 3
;
32 = "the number"
:
:
Check solution in the statement:
"A certain two-digit number has a value that is 2 more than 6 times the sum of its digits. "
32 = 6(3+2) + 2; confirms our solution