This method will work because we can easily multiply any of the equations with a constant that will make the coefficients of x or y to be the same for easy cancellation of one of the variables.
Let the cost adult plate be x
Let the cost of child plate be y
If the girls sold 200 adult dinner plates and 100 child dinner plates for a total cost of $2,150, then;
200x + 100y = 2,150 .................. 1
Similarly, if the boys sold 100 adult dinner plates and 300 child dinner plates for a total cost of $2,625, then;
100x + 300y = 2625 ................ 2
To get the cost of each plate, we will solve equations 1 and 2 simultaneously using the elimination method.
This method will work because we can easily multiply any of the equations with a constant that will make the coefficients of x or y to be the same for easy cancellation of one of the variables.
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