Math worksheet with ratio word problems and answer section.

Problem Analysis:

The task involves solving ratio problems based on the given scenarios. Ratios are expressed as comparisons between two quantities, often written in the form \( a:b \). The goal is to determine missing values or simplify ratios based on the provided information.

Solution to Each Problem:

#### 1) At the malt shop the ratio of hotdogs sold to hamburgers sold was 2:7. For every _____ hamburgers sold there were _____ hotdogs sold.

- Given Ratio: Hotdogs : Hamburgers = 2:7
- Interpretation: For every 7 hamburgers sold, 2 hotdogs were sold.
- Answer: For every 7 hamburgers sold, there were 2 hotdogs sold.

---

#### 2) During the class election the ratio of votes for Haley to votes for Paul was 8:4. For every _____ votes Paul got Haley got _____ votes.

- Given Ratio: Haley : Paul = 8:4
- Simplify the Ratio: Divide both sides by their greatest common divisor (GCD), which is 4.
\[
\frac{8}{4} : \frac{4}{4} = 2:1
\]
- Interpretation: For every 1 vote Paul got, Haley got 2 votes.
- Answer: For every 1 vote Paul got, Haley got 2 votes.

---

#### 3) For every 7 green apples in an orchard there were 9 red apples. What is the ratio of green apples to red apples?

- Given Information: Green Apples : Red Apples = 7:9
- Ratio: The ratio of green apples to red apples is already given as 7:9.
- Answer: The ratio of green apples to red apples is 7:9.

---

#### 4) For every 8 regular sodas a burger shop sold there were 9 diet sodas sold. What is the ratio of regular sodas to diet sodas sold?

- Given Information: Regular Sodas : Diet Sodas = 8:9
- Ratio: The ratio of regular sodas to diet sodas is already given as 8:9.
- Answer: The ratio of regular sodas to diet sodas sold is 8:9.

---

#### 5) At the store the ratio of books sold to movies sold was 3:6. For every _____ books sold there were _____ movies sold.

- Given Ratio: Books : Movies = 3:6
- Simplify the Ratio: Divide both sides by their GCD, which is 3.
\[
\frac{3}{3} : \frac{6}{3} = 1:2
\]
- Interpretation: For every 1 book sold, 2 movies were sold.
- Answer: For every 1 book sold, there were 2 movies sold.

---

#### 6) For every 5 dogs at the pet shelter there are 3 cats. What is the ratio of dogs to cats?

- Given Information: Dogs : Cats = 5:3
- Ratio: The ratio of dogs to cats is already given as 5:3.
- Answer: The ratio of dogs to cats is 5:3.

---

#### 7) In a bag of candy the ratio of chocolate pieces to sugar pieces was 7:2. For every _____ chocolate pieces there are _____ sugar pieces.

- Given Ratio: Chocolate Pieces : Sugar Pieces = 7:2
- Interpretation: For every 7 chocolate pieces, there are 2 sugar pieces.
- Answer: For every 7 chocolate pieces, there are 2 sugar pieces.

---

#### 8) The ratio of boys to girls on a softball team was 5:3. For every _____ girls there are _____ boys.

- Given Ratio: Boys : Girls = 5:3
- Interpretation: For every 3 girls, there are 5 boys.
- Answer: For every 3 girls, there are 5 boys.

---

#### 9) For every 3 rides at the fair there are 4 games. What is the ratio of rides to games?

- Given Information: Rides : Games = 3:4
- Ratio: The ratio of rides to games is already given as 3:4.
- Answer: The ratio of rides to games is 3:4.

---

#### 10) At the thrift store the ratio of long sleeve shirts to short sleeve shirts was 2:8. For every _____ short sleeve shirts there were _____ long sleeve shirts.

- Given Ratio: Long Sleeve Shirts : Short Sleeve Shirts = 2:8
- Simplify the Ratio: Divide both sides by their GCD, which is 2.
\[
\frac{2}{2} : \frac{8}{2} = 1:4
\]
- Interpretation: For every 4 short sleeve shirts, there is 1 long sleeve shirt.
- Answer: For every 4 short sleeve shirts, there were 1 long sleeve shirt.

---

#### 11) The ratio of pickles to onions on a burger was 6:3. For every _____ onions there are _____ pickles.

- Given Ratio: Pickles : Onions = 6:3
- Simplify the Ratio: Divide both sides by their GCD, which is 3.
\[
\frac{6}{3} : \frac{3}{3} = 2:1
\]
- Interpretation: For every 1 onion, there are 2 pickles.
- Answer: For every 1 onion, there are 2 pickles.

---

#### 12) The ratio of Wii games to PS3 games John owned was 2:9. For every _____ PS3 games he owned, he had _____ Wii games.

- Given Ratio: Wii Games : PS3 Games = 2:9
- Interpretation: For every 9 PS3 games, John had 2 Wii games.
- Answer: For every 9 PS3 games, he had 2 Wii games.

---

Final Answers:

1. 7 hamburgers, 2 hotdogs
2. 1 vote, 2 votes
3. 7:9
4. 8:9
5. 1 book, 2 movies
6. 5:3
7. 7 chocolate pieces, 2 sugar pieces
8. 3 girls, 5 boys
9. 3:4
10. 4 short sleeve shirts, 1 long sleeve shirt
11. 1 onion, 2 pickles
12. 9 PS3 games, 2 Wii games

Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
1. \text{7 hamburgers, 2 hotdogs} \\
2. \text{1 vote, 2 votes} \\
3. \text{7:9} \\
4. \text{8:9} \\
5. \text{1 book, 2 movies} \\
6. \text{5:3} \\
7. \text{7 chocolate pieces, 2 sugar pieces} \\
8. \text{3 girls, 5 boys} \\
9. \text{3:4} \\
10. \text{4 short sleeve shirts, 1 long sleeve shirt} \\
11. \text{1 onion, 2 pickles} \\
12. \text{9 PS3 games, 2 Wii games}
\end{array}
}
\]