You are installing 250 feet of PVC conduit. Each 100 -foot section takes $$ \frac{1}{2} $$ can of PVC cement, and each 50 -ft section takes $$ \frac{1}{4} $$ can. How much cement do you need? Your answer should be in the form of a mixed number, with any remaining fraction in its lowest terms. You need $$ \square $$ cans of cemel.

Question

UpStudy AI · Accepted Answer

To determine how much PVC cement is needed for 250 feet of conduit, we can break it down into sections of 100 feet and 50 feet.

1. **Calculate the number of 100-foot sections:**
   - Each 100-foot section requires $$ \frac{1}{2} $$ can of PVC cement.
   - The number of 100-foot sections in 250 feet is:
     $$
     \text{Number of 100-ft sections} = \frac{250}{100} = 2.5
     $$
   - Since we can only have whole sections, we will have 2 full 100-foot sections and 1 remaining 50-foot section.

2. **Calculate the amount of cement for the 100-foot sections:**
   - For 2 sections:
     $$
     \text{Cement for 100-ft sections} = 2 \times \frac{1}{2} = 1 \text{ can}
     $$

3. **Calculate the number of 50-foot sections:**
   - The remaining length after 200 feet (2 sections of 100 feet) is:
     $$
     250 - 200 = 50 \text{ feet}
     $$
   - This is exactly 1 section of 50 feet.

4. **Calculate the amount of cement for the 50-foot section:**
   - For 1 section:
     $$
     \text{Cement for 50-ft section} = 1 \times \frac{1}{4} = \frac{1}{4} \text{ can}
     $$

5. **Total amount of cement needed:**
   - Combine the cement needed for both sections:
     $$
     \text{Total cement} = 1 + \frac{1}{4} = 1 + 0.25 = 1.25 \text{ cans}
     $$

6. **Convert to mixed number:**
   - The total of 1.25 cans can be expressed as a mixed number:
     $$
     1.25 = 1 \frac{1}{4}
     $$

Thus, you need $$ 1 \frac{1}{4} $$ cans of cement.
You need $$ 1 \frac{1}{4} $$ cans of cement.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Arithmetic Questions