Question
After losing 3 baseball cards, Peter gave half of his remaining cards to Bobby. If Peter gave Bobby 9 baseball cards, how many cards did Peter start with?
Linear equation:
1
2
(x - 3) = 9
Bobby claims that Peter started with 21 cards. Which statements are true about verifying Bobby’s claim? Check all that apply.
Substitute 21 for x in the original equation.
Substitute any number for x in the original equation.
Bobby’s claim that x = 21 is correct.
The result of verifying Bobby’s work is 9 = 9.
The result of verifying Bobby’s work is 21 = 21.
Linear equation:
1
2
(x - 3) = 9
Bobby claims that Peter started with 21 cards. Which statements are true about verifying Bobby’s claim? Check all that apply.
Substitute 21 for x in the original equation.
Substitute any number for x in the original equation.
Bobby’s claim that x = 21 is correct.
The result of verifying Bobby’s work is 9 = 9.
The result of verifying Bobby’s work is 21 = 21.
Answers
GPT-4o mini
To solve the problem, let's first verify the original equation:
Given:
Peter lost 3 baseball cards, so if he started with \( x \) cards, he has \( x - 3 \) cards left. Peter then gave half of his remaining cards to Bobby, which is represented as:
\[
\frac{1}{2}(x - 3) = 9
\]
Now, solving for \( x \):
1. Multiply both sides by 2:
\[
x - 3 = 18
\]
2. Add 3 to both sides:
\[
x = 21
\]
Thus, Peter started with 21 baseball cards.
Now, to verify Bobby's claim that Peter started with 21 cards, we can go through the statements:
1. **Substitute 21 for x in the original equation**: **True**. This verifies whether \( x = 21 \) holds true in the equation.
2. **Substitute any number for x in the original equation**: **False**. This does not verify Bobby's specific claim; it only tests if the equation holds for other values.
3. **Bobby’s claim that x = 21 is correct**: **True**. We determined \( x = 21 \) is indeed correct.
4. **The result of verifying Bobby’s work is 9 = 9**: **True**. When substituting \( x = 21 \) into \(\frac{1}{2}(21 - 3) = 9\), it holds true.
5. **The result of verifying Bobby’s work is 21 = 21**: **False**. This statement doesn't apply to the context of verifying the original equation; instead, we compare numerical outcomes (like checking if both sides of an equation are equal).
So, the true statements about verifying Bobby’s claim are:
- Substitute 21 for x in the original equation.
- Bobby’s claim that x = 21 is correct.
- The result of verifying Bobby’s work is 9 = 9.
Given:
Peter lost 3 baseball cards, so if he started with \( x \) cards, he has \( x - 3 \) cards left. Peter then gave half of his remaining cards to Bobby, which is represented as:
\[
\frac{1}{2}(x - 3) = 9
\]
Now, solving for \( x \):
1. Multiply both sides by 2:
\[
x - 3 = 18
\]
2. Add 3 to both sides:
\[
x = 21
\]
Thus, Peter started with 21 baseball cards.
Now, to verify Bobby's claim that Peter started with 21 cards, we can go through the statements:
1. **Substitute 21 for x in the original equation**: **True**. This verifies whether \( x = 21 \) holds true in the equation.
2. **Substitute any number for x in the original equation**: **False**. This does not verify Bobby's specific claim; it only tests if the equation holds for other values.
3. **Bobby’s claim that x = 21 is correct**: **True**. We determined \( x = 21 \) is indeed correct.
4. **The result of verifying Bobby’s work is 9 = 9**: **True**. When substituting \( x = 21 \) into \(\frac{1}{2}(21 - 3) = 9\), it holds true.
5. **The result of verifying Bobby’s work is 21 = 21**: **False**. This statement doesn't apply to the context of verifying the original equation; instead, we compare numerical outcomes (like checking if both sides of an equation are equal).
So, the true statements about verifying Bobby’s claim are:
- Substitute 21 for x in the original equation.
- Bobby’s claim that x = 21 is correct.
- The result of verifying Bobby’s work is 9 = 9.