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:
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:
\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.
