SOLUTION: I've tried to answer this question, but i get one positive solution for apples, and negative solutions for orange & pears, which given the context of the problem, doesn't make sens

Question 953643: I've tried to answer this question, but i get one positive solution for apples, and negative solutions for orange & pears, which given the context of the problem, doesn't make sense (for question #1) ).
> Apple is made up of 20mg zinc, 30mg potassium & 15mg Radium
> Orange is made up of 20mg zinc, 50mg potassium & 10mg radium
> Pear is made up of 20mg zinc, 10mg potassium, & 10mg radium
question #1: you need 115mg zinc, 120mg potassium, 110mg of radium everyday, so how many of each fruit should you eat?
question #2: How many of each fruit do you eat if the mg of zinc in each fruit is cut by 1/2 ?
For #1, I set it up as follows:
FRUIT Apple Orange Pear
Zinc 20 20 20
Potassium 30 50 10
Radium 15 10 10

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
You need a column for question #1, 115,120,110. Try to set up the system of equations first, if that will help you arrange all the necessary elements.

Initially, E1 is for zince E2 for potassium, E3 for Radium.

20, 20, 20, 115
30, 50, 10, 10
15, 10, 10, 110

Try starting with some work between E2 and E3. Subtract half of E2 from one of E3 and revise E3....

Every element can be divided by 5 and you get this matrix:

4, 4, 4, 23
3, 5, 1, 1
3, 2, 2, 22

( ~~I did not yet take further steps with the matrix~~).

I worked through the matrix, and find Pears, , Oranges, . I'm with you. Negative number cannot happen. Problem description is bad.
-
Final matrix was of this form:
4,4, 4, 23
0, 8, -8, -65
0, 0, 1, 27/16
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