The sum of two numbers is 56. the smaller number is 16 less than the larger number. What are the numbers?

Question

Solving a word problem involving a sum and another basic relationship using a system of linear equations 

Answer 1

A.. smaller number 

B.. larger number 

 

A+B = 56 ( sum of two numbers)  eq1

A=B-16 ( small number is 16 less than large number) eq2 

for eq2 is implies to '=' and less than implies to '-'. 

 

 

Using eq2 in eq1 

B-16+B = 56 

2B = 72

B=36 ( larger numbe) 

putting value of B in eq2 ... you can put value of B in eq1. ( either will work) 

 give A= 20 

 

Answer 2

s = smaller number

l = larger number

s + l = 56  eq1

s + 16 = l  eq2

 

substituting eq2 into eq1 and solving for l

s + s + 16 = 56

2s = 40

s = 20

l = 56-20 = 36

So, the smaller number is 20 and the larger number is 36.  They sum to 56 and 20 is 16 less than 36.