Unit Review: Ratios & proportions

E.1Find each unit rate. Write fractions in simplest form.

1. 1
   A hose fills $\frac{5}{6}$ gallon in $\frac{1}{3}$ minute. How many gallons does it fill per minute?
2. 2
   A machine makes $\frac{5}{6}$ pound of pasta in $\frac{1}{4}$ hour. How many pounds does it make per hour?

E.2Do the ratios form a proportion? Write yes or no.

1. 3
   $\frac{10}{15}\stackrel{?}{=}\frac{5}{6}$ 
2. 4
   $\frac{24}{20}\stackrel{?}{=}\frac{30}{25}$ 

E.3Solve each proportion.

1. 5
   $\frac{x}{49}=\frac{2}{14}$
2. 6
   $\frac{35}{y}=\frac{15}{27}$

E.4Write a proportion and solve it.

1. 7
   $3$ gallons of paint cover $1,050$ square feet. How many square feet will $10$ gallons cover?
2. 8
   A club has $3$ boys for every $4$ girls. If there are $12$ boys, how many girls are there?

E.5Find the constant of proportionality, k, for each table.

1. 9
   $\begin{array}{ccccc}x& 1& 2& 3& 4\\ y& 0.4& 0.8& 1.2& 1.6\end{array}$
2. 10
   $\begin{array}{ccccc}x& 6& 10& 14& 18\\ y& 7.5& 12.5& 17.5& 22.5\end{array}$

E.6Write an equation in the form y = kx for each table.

1. 11
   $\begin{array}{ccccc}x& 2& 5& 8& 11\\ y& 5& 12.5& 20& 27.5\end{array}$
2. 12
   $\begin{array}{ccccc}x& 3& 4& 5& 6\\ y& 7.5& 10& 12.5& 15\end{array}$

E.7Is y proportional to x? Write yes or no. If yes, give the constant of proportionality, k.

1. 13
   $y=0.5x+7$
2. 14
   $y=0.25x-7$

E.8Write an equation, then answer the question.

1. 15
   Ben walks $4$ miles per hour. Use $d$ for miles and $t$ for hours. How far does he walk in $2.5$ hours?
2. 16
   Apples cost $\text{\$}3.00$ per pound. Use $c$ for the cost in dollars and $p$ for pounds. What do $7$ pounds cost?

E.9Use the scale to answer each question.

1. 17
   On a blueprint, $1$ inch represents $4$ feet. A room is $1.5$ inches long on the blueprint. How long is the real room?
2. 18
   In a model, $1$ centimeter represents $2$ meters. A model building is $1.5$ centimeters tall. How tall is the real building?

E.10E.11Answer each question.

1. 19
   A triangle has a area of $7$ ft². A scale drawing of it uses a scale factor of $3$. What is the area of the drawing?
2. 20
   A rectangle has a area of $14$ cm². A scale drawing of it uses a scale factor of $4$. What is the area of the drawing?
3. 21
   $\begin{array}{ccccc}x& 2& 4& 6& 8\\ y& 3.6& 7.2& 10.8& 14.4\end{array}$
4. 22
   $\begin{array}{ccccc}x& 2& 4& 6& 8\\ y& 5& 10& 15& 20\end{array}$

E.1Unit Rates with Fractions

1. 1$2\frac{1}{2}$ gallons per minute
2. 2$3\frac{1}{3}$ pounds per hour

E.2Do the Ratios Form a Proportion?

1. 3no
2. 4yes

E.3Solve Proportions

1. 5$x=7$
2. 6$y=63$

E.4Proportion Word Problems

1. 73,500 square feet
2. 816 girls

E.5Constant of Proportionality from a Table

1. 9$k=0.4$
2. 10$k=1.25$

E.6Equations for Proportional Relationships

1. 11$y=2.5x$
2. 12$y=2.5x$

E.7Identify Proportional Relationships

1. 13no
2. 14no

E.8Write & Solve Equations for Proportional Relationships

1. 15$d=4t$; $10$ miles
2. 16$c=3p$; $\text{\$}21.00$

E.9Scale Drawings

1. 176 feet

E.9Scale Drawings (continued)

1. 183 meters

E.10E.11Answer each question.

1. 19$63$ ft²
2. 20$224$ cm²
3. 21$k=1.8$
4. 22$k=2.5$