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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Lloyd's Bakery sold one customer 9 dozen chocolate cookies and 8 dozen oatmeal cookies for $110. The bakery also sold another customer 9 dozen chocolate cookies and 5 dozen oatmeal cookies for $89. How much do the cookies cost?

A dozen chocolate cookies cost $___ and a dozen oatmeal cookies cost $___

Respuesta :

lublana

Answer:

A dozen chocolate cookies cost $6

and a dozen oatmeal cookies cost $7

Step-by-step explanation:

Let cost of 1 dozen chocolate cookies = x

Let cost of 1 dozen oatmeal cookies = y

then we get equations:

9x+8y=110...(i),

and 9x+5y=89...(ii)

Solve equation (i) for x

9x+8y=110

9x=110-8y

[tex]x=\frac{110-8y}{9}[/tex]...(iii)

plug (iii) into (ii)

9x+5y=89

[tex]9\left(\frac{110-8y}{9}\right)+5y=89[/tex]

[tex]110-8y+5y=89[/tex]

[tex]9\left(\frac{110-8y}{9}\right)+5y=89[/tex]

[tex]110-3y=89[/tex]

[tex]-3y=89-110[/tex]

[tex]-3y=-21[/tex]

[tex]y=7[/tex]

plug y=7 into (iii)

[tex]x=\frac{110-8y}{9}=\frac{110-8(7)}{9}=6[/tex]

Hence final answer is given by:

A dozen chocolate cookies cost $6

and a dozen oatmeal cookies cost $7

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