Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Esther the clown does a face painting at the city carnival, she paints $7$ faces every $21$ minutes and spends the same amount of time painting each face. Write an equation that relates $f$ , the number of faces she paints, and $m$ , the time she spends painting in minutes.

View step-by-step help

View step-by-step help

Write a linear function: word problems

Full solution

Q. Esther the clown does a face painting at the city carnival, she paints

7

faces every

21

minutes and spends the same amount of time painting each face. Write an equation that relates

f

, the number of faces she paints, and

m

, the time she spends painting in minutes.

Calculate Rate: Determine the rate at which Esther paints faces. $\newline$ Since Esther paints $7$ faces every $21$ minutes, we can calculate the rate by dividing the number of faces by the time in minutes. $\newline$ Rate = Number of faces / Time in minutes $\newline$ Rate = $7$ faces / $21$ minutes
Simplify Rate: Simplify the rate to find the number of faces painted per minute. $\newline$ To simplify the rate, we divide both the numerator and the denominator by their greatest common divisor, which is $7$ . $\newline$ Rate = $(7 \text{ faces} / 7) / (21 \text{ minutes} / 7)$ $\newline$ Rate = $1 \text{ face} / 3 \text{ minutes}$
Write Equation: Write the equation that relates $f$ , the number of faces painted, to $m$ , the time spent painting. $\newline$ Since the rate is $1$ face per $3$ minutes, we can write the equation as: $\newline$ $f = \frac{1}{3} \cdot m$ $\newline$ This equation shows that for every $3$ minutes, Esther paints $1$ face.

More problems from Write a linear function: word problems

Question

This equation shows how the time required to screen-print a batch of shirts is related to the number of shirts in the batch.

\newline

t = s + 13

\newline

s

represents the number of shirts in the batch, and the variable

t

represents the time required to screen-print the shirts. How long does it take to screen-print a batch of

4

\newline

_________minutes

Posted 2 months ago

Question

Krysta wants to take piano lessons. She asked a teacher how many new pieces she could expect to learn each month. The teacher gave an estimate of

3

. Write an equation that shows how the total number of pieces Krysta would learn,

y

, depends on the number of months of piano lessons,

x

\newline

y

Posted 2 months ago

Question

Tom bought a boat for

\$3,000

and incurs a daily storage fee of

\$15

. Write a linear function to represent the total amount Tom will owe,

p(x)

x

days to pick it up.

\newline

Posted 3 months ago

Question

180

-page book cover to cover in a single session, at a constant rate. It took him

6

\newline

\newline

y

represent the number of pages left to read after

\newline

t

\newline

Which of the following information about the graph of the relationship is given?

\newline

1

\newline

\newline

x

\newline

\newline

y

\newline

(C) Slope and a point that is not an intercept

\newline

\newline

x

\newline

y

\newline

\newline

y

-intercept and a point that is not an intercept

\newline

(F) Two points that are not intercepts

Posted 4 months ago

Question

A charity organization had to sell

18

tickets to their fundraiser just to cover necessary production costs. They sold each ticket for

\$45

y

represent the net profit (in dollars) when they have sold

x

tickets. Which of the following information about the graph of the relationship is given?

\newline

1

\newline

x

\newline

y

\newline

(C) Slope and a point that is not an intercept

\newline

x

y

\newline

y

-intercept and a point that is not an intercept

\newline

(F) Two points that are not intercepts

Posted 2 months ago

Question

Hiro painted his room. After

3

hours of painting at a rate of

8

square meters per hour, he had

28

square meters left to paint.

\newline

\newline

y

represent the area (in square meters) left to paint after

\newline

x

\newline

Which of the following information about the graph of the relationship is given?

\newline

1

\newline

\newline

x

\newline

\newline

y

\newline

(C) Slope and a point that is not an intercept

\newline

\newline

x

\newline

y

\newline

\newline

y

-intercept and a point that is not an intercept

\newline

(F) Two points that are not intercepts

Posted 2 months ago

Question

Naoya read a book cover to cover in a single session, at a rate of

55

pages per hour. After

4

350

pages left to read.

\newline

y

represent the number of pages left to read after

x

\newline

Complete the equation for the relationship between the number of pages left and number of hours.

\newline

y=

Posted 1 month ago

Question

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.

Posted 2 months ago

Question

C=0.25(L-1200)

\newline

C

, in dollars, to the holder of a liability insurance account given a total liability of

L

dollars is given by the equation as long as

C

is positive. By how many dollars does the liability increase when the cost to the holder increases by

1

Posted 2 months ago

Question

P=\frac{2}{5} m+1.5

\newline

P

, in dollars, of a train ticket used to travel a distance of

m

miles is given by the equation. By how many miles does the traveling distance increase if the ticket price increases by

1

Posted 4 months ago