CALCULATING AMOUNTS

Question

Tom, Jan and Sara receive $75. Tom received $8 less than Sara and $5 less than Jan How much did they each receive?

Answer 1

It appears to me that we can approach this problem by placement of quantities (that will add up to exactly 75) along a number-line.

 

Start by placing point S, representing the amount s Sara receives, and then to its left, mark a point T with value s-8, for Tom's lesser amount.

 

Now, about Jan (point J): her amount must be s-3, so that Tom's amount is 5 dollars less than Jan. 

 

Now, let's add up these amounts:  s-8 + s-3 + s = 75.  3s - 11 = 75;  3s = 86.

 

Oh Oh! 86 /3 is an impossible number of dollars (28 and two thirds of one $).

 

So I'm saying the problem is defective (or impossible).  Am I right?

Answer 2

Karen, I think you left out part of your problem. If Tom gets $8 less than Sara and Sara gets $5 less than Jan, then Jan makes $13 more than Tom ($5 more than Sara, who makes $8 more than Tom).

 

t + t + 8 + t + 13 = 75

3t + 21 = 75

3t = 54

t = 18

 

Then Sara got $26 and Jan got $31.

 

The way you typed it is impossible to solve, as pointed out by Kenneth.