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If a tomato and a potato cost $.19, and if a potato and a pepper cost $.16, and if a pepper and a tomato cost $.17, then how much does a tomato cost, how much does a potato cost, and how much does a pepper cost?

Tomato 10, potato 9 , pepper 7?

I dont know how to do it, how did u get those answers?

They were the first ones I tried and they seem to work!

LOL, ok but how did you arrive to those numbers?

The first total you gave was 19 - so I started with 10 +9, then was going to work my way through 9/10, 8/11, 7/12 and so on.

(1) T + Po = 19

(2) Po + Pe = 16

(3) Pe + T = 17

(1) – (3) Po – Pe = 2 (a potato is 2 more than a pepper)

So from (2) a potato must be 9 and a pepper 7, then a tomato is 10

I'm not sure if my algebraic skills are up to the mark but here goes:

Let X = No of tomatoes Let Y = No of potatoes Let Z = No of peppers

X + Y = 19 eq 1
X + Z = 17 eq 2
Y + Z = 16 eq 3
subtract eq 2 from eq 1

Y - Z = 2 eq 4

Add eq 3 & eq 4

2Y = 18 so Y = 9
X + Y = 19 so X = 10
X + Z = 17 so Z = 7

so malone was right. thanks for the help.

Another way of doing this is to note that, if you add together the three initial expressions, each of the three items will appear twice. That is, 2 x (tomato + potato + pepper) = 19 + 16 + 17 = 52, so tomato + potato + pepper = 26.

As tomato + potato = 19, pepper = 26 - 19 = 7.
As potato + pepper = 16, tomato = 26 - 16 = 10.
As pepper + tomato = 17, potato = 26 - 17 = 9.