Answer:
(x, y) = (5, 4)
Step-by-step explanation:
The problem statement defines variables for you:
- x = number of cookies
- y = number of cupcakes
It also gives you two relations between these variables:
- x + y = 9 . . . . . . . . . . . . . . . she bought 9 treats
- 3.75x +4.25y = 35.75 . . . . their total cost was 35.75
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These equations can be solved a number of ways. We can eliminate the x-variable by subtracting 3.75 times the first equation from the second equation:
(3.75x +4.25y) -3.75(x +y) = (35.75) -3.75(9)
0.50y = 2.00 . . . . . simplify
y = 4 . . . . . . . . . . . . .multiply by 2
x = 9-4 = 5 . . . . . . . find x using the first equation
The solution is (x, y) = (5, 4).
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Comment on purchase problems
Problems like this will generally have one of two forms:
- you are given a total quantity and the value of one purchase
- you are given the values of two different purchases
In each case, you are expected to know that the value of the purchase is the sum of products of quantity and price. That is, multiply the number of cookies (x) by the price of a cookie (3.75) and the number of cupcakes (y) by the price of a cupcake (4.25) and add these products together to find the total cost. It should be no mystery, since it is the calculation a store does every time you make a purchase.
Once you have written the equations, you can solve them by any of the available means: elimination, substitution, graphing, Cramer's rule, matrix methods, "guess and check", and so on.
