Question

1. louis owns his own orchard. he plants 9 fruit trees for every 5 nut trees.

the equation $f = \frac{9}{5} n$ models the relationship between the number of nut trees planted and the number of fruit trees planted. determine the number of nut trees planted if 135 fruit trees were planted.

if 135 fruit trees were planted, 75 nut trees were planted.

1. for every $20 you earn, you donate $3 to charity.

the equation $d = \frac{3}{20} e$ models the relationship between the amount earned in dollars and the amount donated in dollars. determine the amount you earned in dollars if you donated $90 to charity.

if you donated $90 to charity, you earned $ \boxed{} .

1. daniel is decorating mirrors from a craft kit he received. he can decorate 9 mirrors every 2 hours.

the equation $h = \frac{2}{9} m$ models the relationship between the number of mirrors decorated and the number of hours. determine the number of mirrors daniel can decorate in 24 hours.

Explanation:

Problem 2

Step1: Identify the equation and given value

We have the equation \( d=\frac{3}{20}e \), and we know that \( d = 90 \) (the amount donated). We need to solve for \( e \) (the amount earned).

Step2: Substitute the value of \( d \) into the equation

Substitute \( d = 90 \) into \( d=\frac{3}{20}e \), we get \( 90=\frac{3}{20}e \).

Step3: Solve for \( e \)

To solve for \( e \), we can multiply both sides of the equation by \( \frac{20}{3} \). So \( e=90\times\frac{20}{3} \). First, calculate \( 90\div3 = 30 \), then \( 30\times20=600 \). So \( e = 600 \).

Step1: Identify the equation and given value

We have the equation \( h=\frac{2}{9}m \), and we know that \( h = 24 \) (the number of hours). We need to solve for \( m \) (the number of mirrors).

Step2: Substitute the value of \( h \) into the equation

Substitute \( h = 24 \) into \( h=\frac{2}{9}m \), we get \( 24=\frac{2}{9}m \).

Step3: Solve for \( m \)

To solve for \( m \), we can multiply both sides of the equation by \( \frac{9}{2} \). So \( m = 24\times\frac{9}{2} \). First, calculate \( 24\div2=12 \), then \( 12\times9 = 108 \). So \( m=108 \).

Answer:

600

Problem 3