Final answer:
To find the length of string Hope used for the third yo-yo, we solve the equation 1\dfrac{3}{4} + 1 + y = 4\dfrac{1}{3} by converting mixed numbers to improper fractions, adding known lengths, and subtracting the sum from the total length to isolate 'y'.
Step-by-step explanation:
The question involves solving a basic algebra equation to find out how much string Hope used for the third yo-yo. Hope has made three yo-yos using strings of different lengths. The equation given, 1\dfrac{3}{4} + 1 + y = 4\dfrac{1}{3}, helps us calculate the length of string used for the third yo-yo, represented by 'y'. To solve for 'y', first, we need to convert mixed numbers to improper fractions, add them, and then isolate 'y' by subtracting the sum from both sides.
1. Start by converting the mixed numbers to improper fractions. The first length of string is 1\dfrac{3}{4} meters, which can be written as \( \frac{7}{4} \) meters. The total length is 4\dfrac{1}{3} meters, which is \( \frac{13}{3} \) meters.
2. To solve for 'y', add the known lengths: \( \frac{7}{4} + 1 \) meters and subtract this sum from the total length \( \frac{13}{3} \) meters.
3. Calculating the sum, we get \( \frac{7}{4} + \frac{4}{4} = \frac{11}{4} \) meters.
4. Subtract \( \frac{11}{4} \) meters from \( \frac{13}{3} \) meters to find 'y'.
Finally, we find that the amount of string used for the third yo-yo is \( y = \frac{13}{3} - \frac{11}{4} \) meters. This calculation requires finding a common denominator and subtracting the fractions properly to determine the length of string 'y'.