A parent has exactly $25 to spend and needs to supply birthday treats to his child’s third-grade class of 32 students. Cupcakes come in boxes of four for $3.80, and doughnuts come six to a bag for $3.00. If each student is to get one such treat (donut or cupcake) and the parent spends exactly $25, determine the number of boxes of cupcakes (x) and bags of doughnuts (y) that need to be purchased for the party. Hint: Set up two simultaneous equations like those in Problem 36.
Problem 36
Consider the equations
5x + 2y = 13 − 3x + 7y = 25
(a) Put each equation into the standard format for a straight line (y = mx + b) and plot both lines. Use your graph to find the point (x, y) where these lines intersect, (b) Use algebra to find the values of x and y that simultaneously satisfy these two equations. (c) How do your answers to parts (a) and (b) compare?
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