Question

Jace and his children went into a bakery and he bought $9 worth of cookies and brownies. Each cookie costs $0.75 and each brownie costs $3. He bought twice as many cookies as brownies. Graphically solve a system of equations in order to determine the number of cookies, x,x, and the number of brownies, y,y, that Jace bought.

Answer 1

Answer:

Step-by-step explanation:

\underline{\text{Variable Definitions:}}

Variable Definitions:

​  

 

x=

x=

\,\,\text{the number of cookies}

the number of cookies

y=

y=

\,\,\text{the number of brownies}

the number of brownies

One cookie costs $0.75, so xx cookies cost 0.75x.0.75x. One brownie costs $3, so yy brownies cost 3y.3y. The total 0.75x+3y0.75x+3y equals \$9:$9:

0.75x+3y=9

0.75x+3y=9

Since Jace bought twice as many cookies as brownies, there are more cookies, so if we multiply 2 by the number of brownies, we will get the number of cookies, meaning xx equals 2y.2y.

x=2y

x=2y

\underline{\text{Write System of Equations:}}

Write System of Equations:

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0.75x+3y=

0.75x+3y=

\,\,9

9

x=

x=

\,\,2y

2y

\underline{\text{Solve for }y\text{ in each equation:}}

Solve for y in each equation:

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\begin{aligned}\color{indianred}{0.75x}+3y = 9\hspace{10px} & \hspace{10px}x=2y \\[10px] 3y = \color{indianred}{-0.75x}+9\hspace{10px} & \hspace{10px}2y=x \\[10px] \frac{3y}{3} = \frac{-0.75x+9}{3}\hspace{10px} & \hspace{10px}\color{green}{y}\color{green}{=}\color{green}{\frac{1}{2}x} \\[10px] \color{blue}{y} \color{blue}{= -\frac{1}{4}x+3}\hspace{10px}\hspace{10px} & \hspace{10px} & \end{aligned}

0.75x+3y=9

3y=−0.75x+9

3

3y

​  

=  

3

−0.75x+9

​  

 

y=−  

4

1

​  

x+3

​  

 

x=2y

2y=x

y=  

2

1

​  

x

​  

 

​  

 

0

the number of cookies

the number of brownies

x

y

(4, 2)

0

the number of cookies

the number of brownies

The xx variable represents the number of cookies and the yy variable represents the number of brownies. Since the lines intersect at the point \left(4, 2\right)(4,2) we can say:

Jace bought 4 cookies and 2 brownies.

Answer 2

Answer:

(9, 18) (3, 6) Plz correct me if wrong

Step-by-step explanation: