Question

the professor is decorating his home and wants to buy some plants. he is interested in three types of plants costing $7, $10, and $13. his budget is $150 and wants to buy 15 plants. translate the information into a system of two linear equations in three variables. find all solutions of the system. specify at least three of his options.

Answer 1

X quantity of first plant which cost $7
y quantity of second plant which cost $10
z quantity of third plant which cost $13

{x+y+z=15
{7x+10y+13z=150
There are 8 solutions with spending $150
Five of them are:
1x$7 +  13x$10 + 1x$13
2x$7  + 11x$10  +2x$13
3x$7 +  9x$10  +3x$13
5x$7  +  5x$10 + 5x$13
6x$7 + 3x$10 + 6x$13