It's to long

Question

Three boys stood on a scale and put a nickel in the slot. The scale showed 390 pounds as their total weight. One boy stepped off the scale. It then showed 255 pounds. The second boy stepped off the scale, and it then showed 145 pounds. Find the weight of each of the three boys.

Answer 1

Let the weights of the tree boys be x, y, and z.

 

The key to solving word (story) problems is to correctly translate the words and phrases of the problem into concise, precise math expressions (with variables and operations).  Let's translate:

 

"scale showed 390 pounds as their total weight"   means   x+y+z = 390     [eq1]

 

"One boy stepped off the scale. It then showed 255 pounds"   means  y+z=255    [eq2]

 

"second boy stepped off the scale, and it then showed 145 pounds"   means z=145   [eq3]

 

The math:

  z=145   [given]

 

  y+z = 255    [eq2 again]

   y+145 = 155     [plug in value from eq3]

   y = 110         [subtract 145 from both sides]

 

  x+y+z = 390                 [eq1 again]

  x + 110 + 145 = 390    [plug in values of y and z]

  x + 255 = 390

  x = 135              [subtract 255 from both sides]

 

Check:

  Is 135+110+145 = 390   ?

        390 = 390   ?yes

 

Answer 2

Hi Brianna,

Let's call the boy that stays on the scale A, the first boy off the scale F, and the second boy off the scale S.

According to the problem, this means:

A+F+S=390

A+S=255

A=145

 

So the boy that stayed on the scale the whole time (A) weighs 145 pounds.

To find the weight of the second boy off the scale (S) we need to substitute 145 into the second equation for A and solve for S.

145+S=255

S=255-145

S=110

 

So the second boy off the scale weighs 110 pounds.

To find the weight of the first boy off the scale (F) we need to substitute each of the other two boys weights into the first equation and solve for F.

145+110+F=390

F=390-145-110

F=135

 

So the first boy off the scale weighs 135 pounds.