Ratio and Proportion Word Problems Worksheet 1 with math exercises and a farmer illustration.

Here are the step-by-step solutions for the problems on your worksheet.

1. A Java book is comprised of two sections core and advanced Java in the ratio 7:2. How much of each type of content will be needed to make a book of 450 pages?
* Step 1: Add the parts of the ratio together to find the total number of "parts" in the book.
$7 + 2 = 9$ parts.
* Step 2: Divide the total number of pages by the total number of parts to find out how many pages are in one part.
$450 \div 9 = 50$ pages per part.
* Step 3: Multiply the value of one part by the specific numbers in the ratio.
Core Java ($7$ parts): $7 \times 50 = 350$ pages.
Advanced Java ($2$ parts): $2 \times 50 = 100$ pages.
* Check: $350 + 100 = 450$. This matches the total.

2. 30 girls and boys have planned for a picnic. There is a ratio of 3 girls to 7 boys. How many boys are there?
* Step 1: Add the ratio parts together.
$3 (\text{girls}) + 7 (\text{boys}) = 10$ total parts.
* Step 2: Find the value of one part.
$30 \text{ students} \div 10 \text{ parts} = 3$ students per part.
* Step 3: Calculate the number of boys (who represent 7 parts).
$7 \times 3 = 21$ boys.

3. 12 miles is approximately equal to 6 km. How many km are equal to 18 miles? How many miles are equal to 42 km?
* Part A (Miles to km):
Notice that 18 miles is exactly double 12 miles ($12 \times 1.5 = 18$ or simpler: $18 \div 12 = 1.5$). Actually, let's look at the relationship: 12 miles = 6 km means 2 miles = 1 km.
So, $18 \text{ miles} \div 2 = 9 \text{ km}$.
* Part B (km to Miles):
Using the same rule (1 km = 2 miles), multiply the kilometers by 2.
$42 \text{ km} \times 2 = 84 \text{ miles}$.

4. 5 pizzas cost \$60. What will 9 pizzas cost?
* Step 1: Find the cost of one pizza (unit price).
$\$60 \div 5 = \$12$ per pizza.
* Step 2: Multiply the unit price by 9.
$9 \times \$12 = \$108$.

5. 6 stuffed peppers cost \$36. What will 12 stuffed peppers cost?
* Method 1 (Unit Price):
Cost of one pepper: $\$36 \div 6