Solve the system as matrix equations using inverses.
-There were 340 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $490. How many adults and how many children attended?
A) 150 adults and 190 children
B) 95 adults and 245 children
C) 122 adults and 218 children
D) 190 adults and 150 children

Question

Quizplus · Accepted Answer

Let x be the number of adults and y be the number of children. The system of equations is:x + y = 3402x + y = 490The matrix form is:[1 1; 2 1] * [x; y] = [340; 490]The inverse of the coefficient matrix is:[1 1; 2 1]^-1 = [-1 1; 2 -1]Multiplying the inverse by the constants gives:[x; y] = [-1 1; 2 -1] * [340; 490] = [150; 190]

Solve the System as Matrix Equations Using Inverses