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Solve a system of equations using any method: word problems

Aaron is purchasing party hats and fake mustaches for an end of the school year party. He can spend at most

\$ 30

. Fake mustaches cost

\$ 3

each, and party hats cost

\$ 2

each. If he must purchase a combination of at least

15

mustaches and party hats, which of the following systems of inequalities best models the relationship between the number of mustaches,

m

, and party hats,

p

\newline

1

\newline

\left\{\begin{array}{l}m+p \geq 15 \\ 3 m+2 p \leq 30\end{array}\right.

\newline

\left\{\begin{array}{l}m+p \leq 15 \\ 3 m+2 p \geq 30\end{array}\right.

\newline

\left\{\begin{array}{l}3 m+2 p \geq 15 \\ m+p \leq 30\end{array}\right.

\newline

\left\{\begin{array}{l}3 m+2 p \leq 15 \\ m+p \geq 30\end{array}\right.

The equation of a circle is

(x-2)^{2}+(y+4)^{2}=36

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(2,4)

and the radius is

6

\newline

(B) The center is

(2,-4)

and the radius is

6

\newline

(C) The center is

(-2,-4)

and the radius is

6

\newline

(D) The center is

(2,-4)

and the radius is

36

A teacher purchased

300

colored pencils for an upcoming project. The pencils she ordered come in packs of

20

30

14

packs in all. Write a system of equations to find the number of

20

(x)

30

(y)

the art teacher ordered.

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

\newline

There are two mystery numbers. The sum of

3

times the first number and

3

times the second number is

-18

2

times the first number and

3

times the second number is

-13

. What are the two numbers?

\newline

The first number is ______ , and the second number is ______.

...