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Answer :
Final answer:
By setting up a system of equations based on the problem statements, we can solve for each variable. We find that a cookie costs around $1.25, while a muffin cost around $1.
Explanation:
This problem is a system of equations where we have two equations, and we're solving for two variables. The variables here are the cost of the cookies and muffins. We can represent the cost of a cookie as 'C' and the cost of a muffin as 'M'.
From the first statement, 'Eight cookies and 3 muffins cost $13', we can form the equation: 8C + 3M = $13.
The second statement, 'Four cookies and six muffins cost $11', gives us the equation: 4C + 6M = $11.
This is a system of equations, and we can solve it by substitution or elimination method. Since these equations are already in a simplified form for the elimination method, we'll multiply the first one by 2 and subtract the second equation from its result:
16C + 6M = $26 (This is 2 times the first equation)
16C - 4C = $26 - $11 which gives 12C = $15
So, a cookie 'C' is $15 divided by 12 or approximately $1.25.
To find the cost of the muffin 'M', we substitute the cost of 'C' into one of our equations, let's use the second one: 4*1.25 + 6M = $11 -> 6M = $11 - $5 -> 6M = $6. So, Muffin 'M' is $6 divided by 6 or $1.
Learn more about System of Equations here:
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Rewritten by : Jeany
Answer:
the cost of each cookie is [tex]\$1.25[/tex]
the cost of each muffin is [tex]\$1.00[/tex]
Step-by-step explanation:
Let
x-----> the cost of each cookie
y----> the cost of each muffin
we know that
[tex]8x+3y=13[/tex] -----> equation A
[tex]4x+6y=11[/tex] -----> equation B
Using a graphing tool
The solution of the system of equations is the intersection point both graphs
The intersection point is [tex](1.25,1)[/tex]
see the attached figure
therefore
the cost of each cookie is [tex]\$1.25[/tex]
the cost of each muffin is [tex]\$1.00[/tex]
