Answer:
cost of a doughnut is $0.75
cost of a cookie is $0.60
Step-by-step explanation:
As you wrote:
Let x = doughnuts
Let y = cookies
The first sentence of the problem (alexandra) can be written as:
[tex]2x + 3y = 3.30[/tex]
The second sentence of the equation (briana) can be written as:
[tex]5x + 2y = 4.95[/tex]
We must now solve for either [tex]x[/tex] or [tex]y[/tex] in this system of equations.
I will solve for [tex]x[/tex] in this example.
First we need to multiply the first equation by [tex]2[/tex] and the second equation by [tex]3[/tex]. This is so both equations have [tex]6y[/tex] as a term.
Equation 1:
[tex]2(2x + 3y) = (3.30)2\\4x + 6y = 6.60[/tex]
Equation 2:
[tex]3(5x + 2y) = (4.95)3\\15x+6y=14.85[/tex]
Now that both equations have [tex]6y[/tex] as a term, we can subtract Equation 1 from Equation 2. This will remove y from the equation and allow us to solve for x.
[tex](15x+6y) - (4x+6y) = (14.85) - (6.60)\\11x = 8.25\\\boxed{x = 0.75}[/tex]
We now know the cost of a doughnut is $0.75. Now we can solve for the cost of a cookie through substitution.
[tex]2x + 3y = 3.30\\2(0.75) + 3y = 3.30\\1.50 + 3y = 3.30\\3y = 1.80\\\boxed{y = 0.6}[/tex]
Now we know the cost of a cookie is $0.60.
These are the answers,
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