Question

A new carpet cleaning company claims that they can clean three times as many carpets in one week as another company. If both companies combine can clean 332 carpets in one week how many carpets does the new company clean?

Answer 1

To calculate how many carpets the new company cleans, we established that if the old company cleans C carpets, the new one cleans 3C. Solving the equation C+3C=332, we find the new company cleans 249 carpets.

Step-by-step explanation:

The subject of the question is Mathematics, specifically involving algebra and systems of equations. The problem presented involves two companies that clean carpets. If the new company can clean three times as many carpets as another company and together they can clean 332 carpets in one week, we are tasked with finding out how many carpets the new company can clean by itself.

Let's denote the number of carpets the older company can clean as C, and thus the new company can clean 3C carpets (since it can clean three times as many). The combined cleaning capability of both companies being 332 carpets can be expressed as:

C + 3C = 332

Solving for C:

1. Combine like terms: 4C = 332
2. Divide both sides by 4: C = 332 / 4
3. C = 83

The original company cleans 83 carpets, and therefore the new company, which cleans three times as many, will clean:

3C = 3 × 83 = 249 carpets