Final answer:
The provided equations in the question do not correctly represent the card's dimensions, as their results contradict the given measurement of the card's width. To solve for the width or length using scale ratios, we must use correct mathematical expressions and consistency in unit measurements is essential.
Step-by-step explanation:
To tackle the problem presented, we need to understand scale ratios, units of measurement, and the process of conversion between these units. First, we'll explore what each option provided in the question means and its correctness.
The first equation, '10 equals one', doesn't provide us with any clear context or relevance to Wilma's card dimensions and thus cannot be evaluated without additional information.
The second equation, '60 equals 1+2×20', suggests that 60 is equal to the sum of 1 and double the width of the card (20 cm). This would be mathematically expressed as 60 = 1 + 2(20). However, this calculation is incorrect because 1 + 2(20) equals 41, not 60.
The third option, '60 = 2×1+2×20', is a mathematical expression stating that 60 is equal to twice 1 plus twice 20. However, this is mathematically incorrect, as 2×1+2×20 equals 42, not 60.
To properly address the ratios given and apply them to solve for the width 'w' in centimeters, we can use the Width scale/actual ratio provided as 'w/10 = 0.5/5'. This ratio forms a proportion where w is the width in centimeters of Wilma's card, and we solve for w as follows:
However, the result here contradicts the initially provided information that the width of Wilma's card is 20 cm. We can infer that there may be a discrepancy or typo in the presented Width scale/actual ratio.
Regarding the conversion between centimeters and meters, the equation '100 cm 1 m' allows us to understand that 100 centimeters is equal to 1 meter. This knowledge is essential when converting measurements from one unit to another. When we divide both sides of the '100 cm = 1 m' equation by 1 meter, we end up with the fraction '100 cm/1 m', which simplifies to 1 because any number divided by itself equals 1. It's a fundamental concept in creating conversion factors in measurements.
In conclusion, none of the provided equations correctly represent the dimensions of Wilma's card. To accurately determine the dimensions of an object using scale ratios, we must use correct mathematical expressions and conversion factors. When working with measurements in a particular unit, it's crucial to ensure consistency across all variables to avoid any confusion or errors.