Respuesta :
Answer:
A bagel costs $1.55, so that would be 155 cents
Step-by-step explanation:
Given Info:
x = cost of a piece of toast
y = cost of a bagel
z = cost of a muffin
2x + y = 3.15
y + z = 3.30
x + 2y + 3z = 9.15
Calculations:
2x + y - (y + z ) = 3.15 - 3.30
2x - z = -0.15
-z = -0.15-2x
z = 0.15+2x
y = 3.15 - 2x
x + 2y + 3z = 9.15
x + 2(3.15 - 2x) + 3(0.15 + 2x) = 9.15
x + 6.3 -4x + 0.45 + 6x = 9.15
3x + 6.75 = 9.15
3x = 2.4
x = 0.80 cents per piece of toast
2x + y = 3.15
2(0.80) + y = 3.15
1.60 + y = 3.15
y = 1.55
So a bagel costs $1.55
One bagel costs 155 cents.
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This question is solved using a system of equations.
I am going to say that:
- x is the cost of a toast.
- y is the cost of a bagel.
- z is the cost of a muffin.
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Two pieces of toast and a bagel costs $3.15.
This means that [tex]2x + y = 3.15[/tex]
Since we want to find the cost of a bagel, we write x as a function of y, so:
[tex]2x = 3.15 - y[/tex]
[tex]x = -0.5y + 1.575[/tex]
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A bagel and a muffin costs $3.30.
This means that:
[tex]y + z = 3.3[/tex]
Since we want y:
[tex]z = 3.3 - y[/tex]
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Piece of toast, two bagels and three muffins cost $9.15.
This means that:
[tex]x + 2y + 3z = 9.15[/tex]
We have x and z as functions of y, so:
[tex]-0.5y + 1.575 + 2y + 3(3.3 - y) = 9.15[/tex]
[tex]-0.5y + 1.575 + 2y + 9.9 - 3y = 9.15[/tex]
[tex]-1.5y + 11.475 = 9.15[/tex]
[tex]1.5y = 2.325[/tex]
[tex]y = \frac{2.325}{1.5}[/tex]
[tex]y = 1.55[/tex]
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In cents, one bagel costs 100*1.55 = 155.
A similar question is found at https://brainly.com/question/24104709
