Unfortunately for you, in this example, life is not that easy. If you are lucky, a variable in each equation will be the opposite of each other and automatically cancel out when adding the equations together (for example, 3 x and -3 x would cancel out). When using the elimination method, the goal is to find a way to remove, or eliminate, a variable by adding the two equations. This reduces a three-equation problem to a two-equation problem - much simpler to solve b 2 b p 7 simplifies to become 3 b p 7.5 b.75(2 b ) 1.25 p 5.25 simplifies to become 2 b 1.25 p 5.25 Weve now managed to remove the o variable from the equations, which helps us move toward a solution, and we can now use the process called elimination, to combine the remaining two equations and temporarily remove the p variable. In this case, we can substitute 2 b for o in the other two equations. Lets use these variables and turn the information in the word problem into mathematical equations: Equation 1: b o p 7 (total number of pieces of fruit) Equation 2: 0.5 b 0.75 o 1.25 p 5.25 (total cost of the fruit, where the number of each piece, indicated by the variable, is multiplied by its individual cost) Equation 3: o 2 b (twice as many oranges as bananas in the mix) Since we know that o 2 b, we can use substitution. However, to avoid confusion, we are going to let b represent the number of bananas used in the drink, o represent the number of oranges, and p represent the number of papayas.
Since you do not know how many of each type of fruit to put in the drink, those are the unknowns for the system of three equations. You also know that the seven pieces of fruit cost 5.25, where bananas cost.50 each, oranges cost.75 each, and papayas cost 1.25 each. You dont know how many of each to put in the punch, but you know that there are seven pieces of fruit in the mix, and there are twice as many oranges as bananas. Tropical Punch Word Problem Suppose you want to make a certain kind of tropical punch, using bananas, oranges, and papayas. The following examples illustrate word problems involving three equations and three unknowns. There are several different methods for solving systems of three equations, and in this lesson we are going to use the two most popular: substitution and elimination.
#Simultaneous equations word problems worksheet how to#
Well explore two different word problem examples of such systems and look at how to set up and solve those systems of equations.Ī system of three equations can be used to solve a problem where there are three unknowns and enough information to make three equations. Simultaneous Equations Word Problems Worksheet How To Set Up Simultaneous Equations Word Problems Worksheet How To Set Up.