Algebra--Integers 3less than 3 times another?

Question

One integer is 3 less than 3 times another integer. If the sum of the two integers is 29, what is the smaller integer??

Answer 1

let a,b be the numbers
a+3=3b
a+b=29

a=29-b
substitute in the first equation
29-b+3=3b
32=4b
b=8 (the smaller integer)

Answer 2

8

Answer 3

8

Answer 4

permit's call "one integer" x, and we are going to call "yet another" y. "One integer is 3 extra advantageous than yet another." this implies "x is 3 extra advantageous than y", or x=3+y. "The sum of their squares is 29." this implies "x squared plus y squared equals 29", or x^2 + y^2 = 29. all of us understand already that x=3+y, so we replace 3+y for x interior the 2d equation to get: (3+y)^2 + y^2 = 29 9+6y+y^2 + y^2 = 29 : enhance 2y^2 + 6y + 9 = 29 : Combining like words 2y^2 + 6y - 20 = 0 : Subtracting 29 from the two factors y^2 + 3y - 10 = 0 : Factoring the two, then dividing it out of the two factors. (y+5)(y-2) = 0 : Factoring So as a result, y=-5 or y=2. If y=-5, then x=y+3, so x=-5+3=-2. If y=2, x=y+3, so x=2+3=5. So the solutions are (x,y)=(5,2) or (-2,-5) -IMP ;) :)

Answer 5

Do the simaltenous equation:



x= 3y-3 [1]
x+y=29 [2]
4y-3=29 [3]
4y=32 [4]
y=8
x=21

Answer 6

x= 3y-3
x+y=29
4y-3=29
4y=32
y=8
x=21