Final answer:
To solve for x in proportion problems, we set up a ratio and cross-multiply. For instance, doubling a 4-inch square side gives 8 inches, and a scale of 1 inch to 2000 miles results in 6,000 miles for 3 inches.
Step-by-step explanation:
To find the value of x in different scenarios, we use proportions which involve setting two ratios equal to each other. For example, if the dimensions of a square are doubled, and the original side length is 4 inches, the new side length is calculated as 4 inches x 2 = 8 inches.
When dealing with scale models, if a 1-inch scale represents 2000 miles, and you know the scale length is 3 inches, the proportion will be set as 1 inch / 2000 miles = 3 inches / x miles. Cross multiplying gives us x = 6000 miles.
Similarly, if the given unit is inches and the proportion is 1 cm / 0.5 m = 150 cm / x m, cross multiplying gives us 0.5 m * 1 cm = 150 cm * x m, solving for x yields x = 0.5 * 150 cm = 75 m.