a grocer sold a total of 126 apples, oranges, and melons one day. she sold 16 fewer oranges than three times as many apples as melons. write a system of three equations that represents how many apples, oranges, and melons the grocer sold
Solve by elimination Method
-x-5y+z=17
-5x-5y+5z=5
2x+5y-3z=-10
To write a system of three equations that represents the number of apples, oranges, and melons the grocer sold, we'll use the given information.
Let's assume the number of apples sold as A, the number of oranges sold as O, and the number of melons sold as M.
1) The total number of fruits sold is 126, so the first equation is:
A + O + M = 126
2) The grocer sold 16 fewer oranges than three times the number of apples as melons. We can express this relationship as:
O = 3A - 16
3) There isn't another direct relation given, so we can assume that any of the variables can be a specific number or have a specific range. However, we can add a constraint that the number of fruits sold cannot be negative:
A ≥ 0, O ≥ 0, M ≥ 0
Therefore, the system of equations representing the grocer's sales is:
A + O + M = 126
O = 3A - 16
A ≥ 0, O ≥ 0, M ≥ 0
By solving this system of equations, you can determine the number of apples, oranges, and melons the grocer sold.