SOLUTION: A catering service placed an order for eight centerpieces and five glasses, and the bill was $106. For the wedding reception it was short one centerpiece and six glasses and had to
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Question 264486: A catering service placed an order for eight centerpieces and five glasses, and the bill was $106. For the wedding reception it was short one centerpiece and six glasses and had to reorder. This order came to $24. Let x represent the cost of one centerpiece, and let y represent the cost of one glass.
Write an equation using x and y that represents the cost of the first order.
Write an equation using x and y that represents the cost of the second order.
The equations in parts a and b form a system of two linear equations that can be used to determine the cost of a single centerpiece and a single glass. Write this system below.
Solve the system using the substitution method.
Use the addition method to check your result in part d.
Use the solution to the system to determine the cost of 15 centerpieces and 10 glasses.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A catering service placed an order for eight centerpieces and five glasses, and the bill was $106. For the wedding reception it was short one centerpiece and six glasses and had to reorder. This order came to $24. Let x represent the cost of one centerpiece, and let y represent the cost of one glass.
Write an equation using x and y that represents the cost of the first order.
Let x = cost of a centerpiece
Let y = cost of a glass
8x + 4y = 106
------------------------------------
Write an equation using x and y that represents the cost of the second order.
x + 6y = 24
---------------------------
The equations in parts a and b form a system of two linear equations that can be used to determine the cost of a single centerpiece and a single glass. Write this system below.
8x+4y = 106
x + 6y = 24
----------------------
Solve the system using the substitution method.
x = 24-6y
8(24-6y)+4y = 106
8*24 - 48y+4y = 106
44y = 192-106
y = $1.95 (cost of a glass)
Since x = 24-6y , x = $12.27 (cost of a centerpiece)
Use the addition method to check your result in part d.
8x+4y = 106
x + 6y = 24
---
8x+4y = 106
8x+48y = 8*24
----
44y = 86
y = same as above
x = same as above
------------------------
Use the solution to the system to determine the cost of 15 centerpieces and 10 glasses.
15*cost of centerpiece + 10*cost of a glass = your answer
==================
Cheers,
Stan H.
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