Ratio and Rates Word/Story Problems - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

1) Bob has 12 red cards and 20 green cards. What is the ratio of Bob’s red cards to his green cards?
* Step 1: Write down the number of red cards first, then the number of green cards: $12$ to $20$.
* Step 2: Simplify the ratio. Both numbers can be divided by $4$.
* $12 \div 4 = 3$
* $20 \div 4 = 5$
* Result: The simplified ratio is $3:5$.

2) In a party, 10 soft drinks are required for every 12 guests. If there are 252 guests, how many soft drinks is required?
* Step 1: Set up a proportion. Let $x$ be the number of soft drinks needed.
$$\frac{10 \text{ drinks}}{12 \text{ guests}} = \frac{x \text{ drinks}}{252 \text{ guests}}$$
* Step 2: Solve for $x$. You can cross-multiply or find out how many groups of 12 are in 252.
* $252 \div 12 = 21$ (There are 21 groups of guests).
* Multiply that by the drinks per group: $21 \times 10 = 210$.
* Result: $210$ soft drinks.

3) In Jack's class, 18 of the students are tall and 10 are short. In Michael's class 54 students are tall and 30 students are short. Which class has a higher ratio of tall to short students?
* Step 1: Find the ratio for Jack's class (Tall : Short).
* $18 : 10$. Divide both by $2$ to simplify $\rightarrow 9 : 5$.
* Step 2: Find the ratio for Michael's class (Tall : Short).
* $54 : 30$. Divide both by $6$ to simplify $\rightarrow 9 : 5$.
* Step 3: Compare them. Since $9:5$ is equal to $9:5$, the ratios are the same.
* Result: Neither; they have the same ratio.

4) The price of 3 apples at the Quick Market is $\$1.44$. The price of 5 of the same apples at Walmart is $\$2.50$. Which place is the better buy?
* Step 1: Find the unit price (price per apple) at Quick Market.
* $\$1.44 \div 3 = \$0.48$ per apple.
* Step 2: Find the unit price at Walmart.
* $\$2.50 \div 5 = \$0.50$ per apple.
* Step 3: Compare prices. $\$0.48$ is cheaper than $\$0.50$.
* Result: Quick Market.

5) The bakers at a Bakery can make 160 bagels in 4 hours. How many bagels can they bake in 16 hours? What is that rate per hour?
* Step 1 (Rate per hour): Divide total bagels by total hours.
* $160 \div 4 = 40$ bagels per hour.
* Step 2 (Total in 16 hours): Multiply the hourly rate by 16 hours.
* $40 \times 16 = 640$ bagels.
* Result: They can bake $640$ bagels. The rate is $40$ bagels per hour.

6) You can buy 5 cans of green beans at a supermarket for $\$3.40$. How much does it cost to buy 35 cans of green beans?
* Step 1: Figure out how many "sets" of 5 cans are in 35 cans.
* $35 \div 5 = 7$ sets.
* Step 2: Multiply the price of one set by 7.
* $\$3.40 \times 7 = \$23.80$.
* Result: $\$23.80$.

7) The ratio of boys to girls in a class is 2:3. If there are 18 boys in the class, how many girls are in that class?
* Step 1: Look at the boys' part of the ratio ($2$). We know this represents $18$ actual boys.
* Step 2: Find the multiplier. How many times does $2$ go into $18$?
* $18 \div 2 = 9$.
* Step 3: Apply that multiplier to the girls' part of the ratio ($3$).
* $3 \times 9 = 27$.
* Result: $27$ girls.

8) The ratio of red marbles to blue marbles in a bag is 3:4. If there are 42 marbles in the bag, how many of the marbles are red?
* Step 1: Add the parts of the ratio together to find the total number of "parts."
* $3 + 4 = 7$ parts total.
* Step 2: Divide the total number of marbles by the total parts to find the value of one part.
* $42 \div 7 = 6$ marbles per part.
* Step 3: Multiply the value of one part by the red marble ratio number ($3$).
* $3 \times 6 = 18$.
* Result: $18$ red marbles.

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Final Answer:
1) 3:5
2) 210 soft drinks
3) Neither (the ratios are equal)
4) Quick Market
5) 640 bagels; 40 bagels per hour
6) $23.80
7) 27 girls
8) 18 red marbles