Answer:
x=30
Step-by-step explanation:
x = x
half of x = (1/2) x = "its half"
third of x = (1/3) x = "its third"
"A number x when added to its half" = x + (1/2)x
"its third increased by 35" = (1/3)x + 35
according to the prompt, these two are equal, so
x + (1/2) x = (1/3)x + 35
x = 1x = (2/2)x to match denominators
(2/2)x + (1/2)x = (1/3)x + 35
= (3/2)x
(3/2)x = (1/3)x + 35
subtract (1/3)x from both sides to isolate the variable and its coefficients
(3/2)x - (1/3)x = 35
multiply both sides by 6 as that is the lowest common multiple of both 2 and 3 (2*3 = 6 so 6 is a multiple of both)
9x - 2x = 35*6
7x = 210
divide both sides by 7 to isolate x
x = 30
