The sum of three integers is 189. The first integer is 28 less than the second. The second integer is 21 less than the sum of the first and third integer. Find the three integers

Answer:The first integer is 56The second integer is 84The third integer is 49Step-by-step explanation:Define the variablesLetx ----> the first integery ----> the second integerz ----> the third integerwe know that[tex]x+y+z=189[/tex] ----> equation A[tex]x=y-28[/tex] ----> [tex]y=x+28[/tex] ----> equation B[tex]y=(x+z)-21[/tex] ----> equation CEquate equations B and C[tex](x+z)-21=x+28[/tex]subtract x both sides[tex]z-21=28[/tex]Adds 21 both sides[tex]z=28+21[/tex][tex]z=49[/tex]substitute the value of z in equation A[tex]x+y+49=189[/tex] [tex]x+y=189-49[/tex] [tex]x+y=140[/tex] -----> equation DSolve the system of equations B and D[tex]y=x+28[/tex] ----> equation B[tex]x+y=140[/tex] -----> equation Dsubstitute equation B in equation D and solve for x[tex]x+x+28=140[/tex][tex]2x+28=140[/tex][tex]2x=140-28[/tex][tex]2x=112[/tex][tex]x=56[/tex]Find the value of y[tex]y=x+28[/tex] -----> [tex]y=56+28=84[/tex]thereforeThe first integer is 56The second integer is 84The third integer is 49