Integrated algebra

Question

The sum of three integers is 194.the sum of the first and second integers exceeds the third by 80.the third integer is 45 less than the first.find the three integers

Answer 1

m, n, and p are the 3 integers.  The given information translates into algebra as

 

(i)    m + n + p = 194

 

(ii)   (m + n) = p + 80

 

(iii)  p = m - 45

 

Plug (ii) into (i) and get

 

(p + 80) + p = 194

2p = 194 - 80 = 114

p = 114/2 = 57

 

p = 57

 

Plug p = 57 into (iii) and get

 

57 = m - 45

m = 57 + 45 = 102

 

m = 102

 

Plug answers for m and p into (i) and get

 

102 + n + 57 = 194

 

n = 194 - (102 + 57) = 35

 

n = 35

 

Test the answers.