Systems of Equations and Inequalities

[ssummer69]

I am having a hard time with this problem:
The perimeter of a triangle is 105 inches. The longest side is 22 inches longer than the shortest side. The sum of the lengths of the two shorter sides is 15 inches more than the length of the longest side. Find the lengths of the sides of the triangle.

 

[arthur ohlsten]

the 3 sides in order of lengths are a,b,c

a+b+c=105

a=c+22

b+c=15+a

from eq2 c=22-a substitute into eq 1
a+b+22-a=105
b=83 answer

from eq 3
83+22-a =15 +a
105-15=2a
a=45 answer

a=c+22
c=23 answer

Arthur

 

[Deleted member 4993]

the 3 sides in order of lengths are a,b,c

a+b+c=105

a=c+22

b+c=15+a

from eq2 c=22-a substitute into eq 1<<< Incorrect it should be c = a - 22
a+b+22-a=105
b=83 answer <<< Really!!! and "b" is the middle length and the perimeter is 105??

from eq 3
83+22-a =15 +a
105-15=2a
a=45 answer

a=c+22
c=23 answer

Let' add them up a+b+c = 83+45+23 = 151 <<< doesn't match equation (1)

Arthur

Answers are wrong - however, the method is correct

 

[arthur ohlsten]

Sorry if I made a error. I should have checked
1) a+b+c=105
2)a=c+22
3) b+c=15+a

substitute eq2) into eqs 1&3
eq4) c+22+b+c=105
eq4) 2c+b=83

eq5) b+c=15+c+22
eq5) b=37 answer

from eq4) 2c+37=83
2c=46
c=23 answer

eq1) a+37+23=105
a=45 answer

Arthur

sorry, but of course you should do the work yourself.