Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
p and
q vary inversely and
p is 8 when
q is 21 , determine
q when
p is equal to 84 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $8$ when $q$ is $21$ , determine $q$ when $p$ is equal to $84$ . $\newline$ Answer:

View step-by-step help

View step-by-step help

Write and solve inverse variation equations

Full solution

Q. If

p

and

q

vary inversely and

p

is

8

when

q

is

21

, determine

q

when

p

is equal to

84

.

\newline

Answer:

Understand relationship: Understand the relationship between $p$ and $q$ . Since $p$ and $q$ vary inversely, we can write the relationship as $p = \frac{k}{q}$ , where $k$ is the constant of variation.
Find constant of variation: Use the given values to find the constant of variation $k$ . We know that $p = 8$ when $q = 21$ . Substitute these values into the inverse variation equation $p = \frac{k}{q}$ . $8 = \frac{k}{21}$
Solve for k: Solve for k. $\newline$ Multiply both sides by $21$ to isolate $k$ . $\newline$ $8 \times 21 = k$ $\newline$ $k = 168$
Write variation equation: Write the inverse variation equation with the found value of $k$ . Now that we have $k = 168$ , the equation becomes $p = \frac{168}{q}$ .
Find $q$ for $p=84$ : Find $q$ when $p$ is equal to $84$ . Substitute $p = 84$ into the equation $p = \frac{168}{q}$ . $84 = \frac{168}{q}$
Solve for q: Solve for q. $\newline$ Multiply both sides by $q$ and then divide by $84$ to isolate $q$ . $\newline$ $84q = 168$ $\newline$ $q = \frac{168}{84}$ $\newline$ $q = 2$

More problems from Write and solve inverse variation equations

Question

In a direct variation,

y = 6

x = 2

. Write a direct variation equation that shows the relationship between

x

y

\newline

Write your answer as an equation with

y

first, followed by an equals sign.

Posted 5 months ago

Question

y

varies directly with

x

y = 12

x = 6

y

x = 4

\newline

Write and solve a direct variation equation to find the answer.

\newline

y =

Posted 5 months ago

Question

Which equation shows inverse variation?

\newline

\newline

(\frac{x}{36}) = y

\newline

yx = -74

Posted 5 months ago

Question

y

varies inversely with

x

y = 1

x = 4

y

x = 2

\newline

Write and solve an inverse variation equation to find the answer.

\newline

y =

Posted 5 months ago

Question

What is the value of

\frac{x^{2}}{y^{4}}

x=8

y=2

Posted 5 months ago

Question

(x+4)(2 x-a)=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=4

x=-4

, what is the value of

a

Posted 3 months ago

Question

(2 x+5)(-m x+9)=0

\newline

In the given equation,

m

is a constant. If the equation has the solutions

x=-\frac{5}{2}

x=\frac{3}{2}

, what is the value of

m

Posted 3 months ago

Question

(4 x+3)-(5 x-7)=a x+b

\newline

In the given equation,

b

is a constant. What is the value of

b

Posted 3 months ago

Question

y=\frac{29}{8} x-\frac{2}{3}

\newline

The given equation is graphed in the

x y

-plane. What is the slope of the line?

Posted 8 months ago

Question

a t^{2}+\frac{7}{2} t-4=0

\newline

The given equation has solutions at

t=-8

t=1

. What is the value of the constant

a

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant