The integers a,b and c satisfy the equations a+5=b, 5+b=c, and b+c=a. What is the value of b?
A number or a short expression. Spacing and $ signs are ignored.
Solutions — 2
Solution 1
Since a+5=b, then a=b−5. Since a=b−5 and c=5+b and b+c=a, then b+(5+b)=b−5, 2b+5=b−5, b=−10. (If b=−10, then a=b−5=−15 and c=5+b=−5 and b+c=(−10)+(−5)=(−15)=a, as required.)
Solution 2
Since a+5=b, then a=b−5. Substituting a=b−5 and c=5+b into b+c=a, we obtain b+(5+b)=b−5. Simplifying, we get 2b+5=b−5, which gives b=−10.
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