Height word problem

Question

Three of Santa's helpers are a combined height of eleven feet and three inches. William is twelve inches shorter than Timothy, who is nine inches taller than James. How tall is each of Santa's helpers?

Answer 1

Hi Phil, 

We can solve this problem through the following steps: 

Step One: Since we know that out total height is 11ft3inches, we can convert to inches. 12 inches are in one foot, so:

Total height in inches=11ft+3inches

Total height in inches=(12)(11)+3

Total height in inches=132+3                        

Total height in inches=135

Step Two: We can translate the heights of Santa's helpers into Let Statements:

Let Will's height in inches= (x+9)-12

Let Tim's height in inches= x+9

Let James's height in inches= x

Step Three: Create our equation and solve:

Will's height in inches+Tim's height in inches+James's height in inches=Total height

x+x+9+(x+9)-12=135

2x+9+x+9-12=135

3x+18-12=135

3x+6=135

3x=135-6

3x=129

x=43

∴James is 43 inches, Time is 52 inches, and Will is 40 inches.

Best, 

Star