Final answer:
To find the total number of words required for the project, we set up a proportion where Diego has written 3/5 of the total. Multiplying 800 by the reciprocal of 3/5 gives us 1334 words, which is the approximate number of words required for their project.
Step-by-step explanation:
Diego and Han are working on their writing project, and we need to know how many words are required in total. Diego says he has written 3 over 5 of the required number of words, which translates to ⅓ of the total word count. Given that Diego has written 800 words, we can set up a proportion to solve for the total number of words needed.
Letting x represent the total number of words required for the project, we can write the following equation based on the proportion Diego provided:
⅓ of x = 800 words
To find x, we multiply both sides of the equation by ⅕, the reciprocal of ⅓:
x = 800 words × ⅕
Calculating this, we get:
x = 800 words × 5 ÷ 3
x = (800 × 5) ÷ 3
x = 4000 ÷ 3
x = 1333.⅓ words
Since we can't have a fraction of a word in this context, we round up to the nearest whole number, suggesting that the total word count required is approximately 1334 words. We also know that Han has written 200 more words than Diego, which means he has written 1000 words, but this additional information is not required to answer the question.