A decorator wants to purchase plants for a new home She is i

A decorator wants to purchase plants for a new home. She is interested in three types of plants costing $7, $10, and $13 each. If she has budgeted exactly $150 for the plants and wants to purchase exactly 15 of them, what are her options? List or make a chart of ALL options.

Solution

Let us assume that

a= number of $13 plants

b= number of $7 plants and

c= number of $10 plants

Now the condition is that a+b+c=15

(a*13) +(b*7)+(c*10)=150

From trial and error method

assume

a=1, b=1,c=13

a+b+c=15

and (1*13)+(1*7)+(13*10)=150

similarly

a=2, b=2, c=11

a+b+c=15

(2*13)+(2*7)+(11*10)=150

similarly a=3,b=3,c=9

3+3+9=15

and (3*13)+(3*7)+(9*10)=150

similarly a=4,b=4,c=7

4+4+7=15

(4*13)+(4*7)+(7*10)=150

similarly a=5, b=5, c=5

(5*13)+(5*7)+(5*10)=150

similarly a=6,b=6,c=3

(6*13)+(6*7)+(3*10)=150

similarly a=7,b=7,c=1

(7*13)+(7*7)+(1*10)=150