Word problems

Question

The Tigers won eight games more then they lost and there were no ties if the Tigers played a total of 78 games how many games did they lose? 

Find three consecutive integers whose sum is 126?

Answer 1

The Tiger problem:

 

Lets start by defining a few variables. 

We will say that W stands for wins and L stand for losses. 

 

The word problem is saying that the Tigers won 8 more games than they lost.

So W = L + 8

 

Because there were no ties we also know that W + L = 78

We can substitute the first equation into the second one to get L + 8 + L = 78

Simpliy:

 

2L = 70

L = 35

 

The Tigers lost 35 games.

 

The sum problem:

 

Lets start with the integer n as the first integer. We can then conclude that n + (n+1) + (n+2)  = 126. (n+1) and (n+2) represent the consecutive integers and we know that if we add them all up they must equal 126. Now all we have to do is simplifiy:

 

n + (n+1) + (n+2) = 126

3n + 3 = 126

3n = 123

n = 41

 

Our 3 consecutive numbers are 41, 42 and 43