Question

Four cookies and three cupcakes code $13.25. Five cookies and two cupcakes cost $11.75. Give the system of equations that could be used to find the cost of one cookie and the cost of one cupcake. Solve the system.

Answer 1

• cookie: $1.25
• cupcake: $2.75

Explanation:

Let x and y represent the cost of a cookie and a cupcake, respectively.

4x +3y = 13.25

5x +2y = 11.75 . . . . . . the system of equations

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By Cramer's rule:

x = (3(11.75) -2(13.25))/(3(5) -2(4)) = 8.75/7 = 1.25

y = (13.25(5) -11.75(4))/7 = 19.25/7 = 2.75

The cost of one cookie is $1.25; the cost of one cupcake is $2.75.

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Cramer's rule gives the solution to the system of equations ...

ax +by =c

dx +ey = f

as ...

∆ = bd -ea

x = (bf -ec)/∆

y = (cd -fa)/∆