you have 3.75 to spend at a vending machine. You want to buy at least three health bars. Regualr health bars cost 0.75 each and strawberry health bar cost 1.25 each. Write a sysem of equtions that represents the situation?

Let x be the number of regular health bars you buy and y the number of strawberry health bars you buy. Then:

0.75x+1.25y=3.75

x+y>=3

Step-by-step explanation:

For the first equation, we have to assume that you will spend all of your money, otherwise it becomes an inequation. The money you spend on regular bars is 0.75x dollars and the money you spend on strawberry bars is 1.25y, so if you spend your 3.75 dollars on the bars, then 0.75x+1.25y=3.75.

For the second, you will always buy x+y health bars, regular and strawberry. There isn't enough information to make this into a equation, the only thing we can deduce is the inequation x+y>=3.

If we also assume that x and y are integers (we can't buy half-bars or one-fourth of a bar) then the minimum number of bars we can buy is 3 (3 strawberry bars) and the maximum is 5 bars (5 regular bars). x+y must be an integer too, so the possibilities for the second equation are x+y=3, x+y=4 and x+y=5. There is a finite number of solutions in any case.