Mark and Joe are eating pizzas and burgers. Mark ate 3/4 of a pizza and 1/2 of a burger, which together is equivalent to 7/8 of the total food consumed. Joe ate 1/4 of a pizza and 3/4 of a burger, which together is equivalent to 5/8 of the total food consumed. If the total amount of food they ate is represented by the variable “x,” write a system of simultaneous equations to represent this situation.
Let the total amount of food they ate be represented by the variable "x".
Mark ate 3/4 of a pizza, so that is 3/4 * x = 3x/4.
Mark also ate 1/2 of a burger, so that is 1/2 * x = x/2.
Together, Mark ate 3x/4 + x/2 = 7/8 of the total food consumed.
Joe ate 1/4 of a pizza, so that is 1/4 * x = x/4.
Joe also ate 3/4 of a burger, so that is 3/4 * x = 3x/4.
Together, Joe ate x/4 + 3x/4 = 5/8 of the total food consumed.
Therefore, the system of simultaneous equations is:
3x/4 + x/2 = 7/8
x/4 + 3x/4 = 5/8