Question
Dan painted 3/4of a wall using 1/4of a can of paint. Which statements are true? Select all that apply. a He can paint 1 wall with 1/3can of paint. b He can paint 2 walls with 1/2can of paint. c He can paint 3 walls with 1 can of paint. d He can paint 5 walls with 1 2/3cans of paint. e He can paint 8 walls with 2 cans of paint.
Answers
GPT-4o mini
To understand the statements, we first need to determine Dan's rate of painting based on the information given:
Dan painted \( \frac{3}{4} \) of a wall using \( \frac{1}{4} \) of a can of paint.
1. **Determine how many walls Dan can paint with 1 can of paint:**
- If \( \frac{1}{4} \) can paints \( \frac{3}{4} \) of a wall, then using all 1 can of paint, we can set up a proportion to find out how many walls he can paint with 1 can.
- The rate of walls per can is:
\[
\text{Walls per can} = \frac{\frac{3}{4} \text{ wall}}{\frac{1}{4} \text{ can}} = \frac{3}{4} \times \frac{4}{1} = 3 \text{ walls}
\]
So, Dan can paint 3 walls with 1 can of paint.
2. **Now, let's evaluate each statement:**
a. **He can paint 1 wall with 1/3 can of paint.**
- To paint 1 wall, he needs \( \frac{1}{3} \) can:
\[
\text{Amount of paint needed for 1 wall} = \frac{1 \text{ wall}}{\text{3 walls per can}} = \frac{1}{3} \text{ can}
\]
This statement is **true**.
b. **He can paint 2 walls with 1/2 can of paint.**
- To paint 2 walls, he needs:
\[
\text{Amount of paint needed for 2 walls} = \frac{2 \text{ walls}}{3 \text{ walls per can}} = \frac{2}{3} \text{ can}
\]
This statement is **false**.
c. **He can paint 3 walls with 1 can of paint.**
- We already calculated that he can paint 3 walls with 1 can of paint.
This statement is **true**.
d. **He can paint 5 walls with 1 2/3 cans of paint.**
- To paint 5 walls, he needs:
\[
\text{Amount of paint needed for 5 walls} = \frac{5 \text{ walls}}{3 \text{ walls per can}} = \frac{5}{3} \text{ can} = 1 \frac{2}{3} \text{ cans}
\]
This statement is **true**.
e. **He can paint 8 walls with 2 cans of paint.**
- To paint 8 walls, he needs:
\[
\text{Amount of paint needed for 8 walls} = \frac{8 \text{ walls}}{3 \text{ walls per can}} = \frac{8}{3} \text{ can} \approx 2.67 \text{ cans}
\]
This statement is **false**.
**Summary of the true statements:**
- a. True
- c. True
- d. True
Thus, the true statements are:
**a, c, and d.**
Dan painted \( \frac{3}{4} \) of a wall using \( \frac{1}{4} \) of a can of paint.
1. **Determine how many walls Dan can paint with 1 can of paint:**
- If \( \frac{1}{4} \) can paints \( \frac{3}{4} \) of a wall, then using all 1 can of paint, we can set up a proportion to find out how many walls he can paint with 1 can.
- The rate of walls per can is:
\[
\text{Walls per can} = \frac{\frac{3}{4} \text{ wall}}{\frac{1}{4} \text{ can}} = \frac{3}{4} \times \frac{4}{1} = 3 \text{ walls}
\]
So, Dan can paint 3 walls with 1 can of paint.
2. **Now, let's evaluate each statement:**
a. **He can paint 1 wall with 1/3 can of paint.**
- To paint 1 wall, he needs \( \frac{1}{3} \) can:
\[
\text{Amount of paint needed for 1 wall} = \frac{1 \text{ wall}}{\text{3 walls per can}} = \frac{1}{3} \text{ can}
\]
This statement is **true**.
b. **He can paint 2 walls with 1/2 can of paint.**
- To paint 2 walls, he needs:
\[
\text{Amount of paint needed for 2 walls} = \frac{2 \text{ walls}}{3 \text{ walls per can}} = \frac{2}{3} \text{ can}
\]
This statement is **false**.
c. **He can paint 3 walls with 1 can of paint.**
- We already calculated that he can paint 3 walls with 1 can of paint.
This statement is **true**.
d. **He can paint 5 walls with 1 2/3 cans of paint.**
- To paint 5 walls, he needs:
\[
\text{Amount of paint needed for 5 walls} = \frac{5 \text{ walls}}{3 \text{ walls per can}} = \frac{5}{3} \text{ can} = 1 \frac{2}{3} \text{ cans}
\]
This statement is **true**.
e. **He can paint 8 walls with 2 cans of paint.**
- To paint 8 walls, he needs:
\[
\text{Amount of paint needed for 8 walls} = \frac{8 \text{ walls}}{3 \text{ walls per can}} = \frac{8}{3} \text{ can} \approx 2.67 \text{ cans}
\]
This statement is **false**.
**Summary of the true statements:**
- a. True
- c. True
- d. True
Thus, the true statements are:
**a, c, and d.**