Esther the Clown does 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 of Painting: Esther paints 7 faces every 21 minutes. To find the relationship between the number of faces (f) and the time in minutes (m), we need to determine the rate at which she paints faces per minute. We can calculate this rate by dividing the number of faces she paints by the time it takes to paint them. Calculation: Rate of painting = Number of faces painted / Time in minutes = 7 faces / 21 minutesWrite Equation: After calculating the rate, we find that Esther paints 1 face every 3 minutes (7 faces / 21 minutes = 1 face / 3 minutes). This rate can be used to write the equation that relates the number of faces painted (f) to the time spent painting (m). The equation is: f = (m/3)Check Equation: To ensure that the equation is correct, we can check it by substituting the values from the given information. If Esther paints 7 faces in 21 minutes, then by substituting m = 21 into the equation f = (m/3), we should get f = 7. Calculation: f = (21/3) = 7

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Esther the Clown does face painting at the city carnival. She paints $7$ faces every $21$ minutes and spends the same amount of time painting each face. $\newline$ 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

Home

Math Problems

Algebra 1

Solve a system of equations using substitution: word problems

Full solution

Q. Esther the Clown does face painting at the city carnival. She paints

7

faces every

21

minutes and spends the same amount of time painting each face.

\newline

Write an equation that relates

f

, the number of faces she paints, and

m

, the time she spends painting in minutes.

Calculate Rate of Painting: Esther paints $7$ faces every $21$ minutes. To find the relationship between the number of faces ( $f$ ) and the time in minutes ( $m$ ), we need to determine the rate at which she paints faces per minute. We can calculate this rate by dividing the number of faces she paints by the time it takes to paint them. $\newline$ Calculation: Rate of painting = Number of faces painted / Time in minutes = $\frac{7 \text{ faces}}{21 \text{ minutes}}$
Write Equation: After calculating the rate, we find that Esther paints $1$ face every $3$ minutes ( $7$ faces / $21$ minutes = $1$ face / $3$ minutes). This rate can be used to write the equation that relates the number of faces painted ( $f$ ) to the time spent painting ( $m$ ). $\newline$ The equation is: $f = \frac{m}{3}$
Check Equation: To ensure that the equation is correct, we can check it by substituting the values from the given information. If Esther paints $7$ faces in $21$ minutes, then by substituting $m = 21$ into the equation $f = (m/3)$ , we should get $f = 7$ . $\newline$ Calculation: $f = (21/3) = 7$