<span><span>Let x = the 10's digit Let y - units digit then 10x + y = original number : Write and equation for each statement: ; "the units digits of a two-digit number is 3 more than twice the tens digit." y = 2x + 3 : "If the digits are reversed, the new number is 9 less than 4 times the original number." 10y + x = 4(10x+y) - 9 10y + x = 40x + 4y - 9 10y - 4y = 40x - x - 9 6y = 39x - 9 :
Find the original number. : Substitute (2x+3) for y in the above equation: 6(2x+3) = 39x - 9 12x + 18 = 39x - 9 18 + 9 = 39x - 12x 27 = 27x x = 1 : Then using y = 2x+3 y = 2(1) + 3 y = 5 : Original number = 15 : : Check solution in the statement: "If the digits are reversed, the new number is 9 less than 4 times the original number." 51 = 4(15) - 9</span><span> </span></span>