Question

1. justin has 26 cards and his younger brother has 11 cards. their mother wants justin to hand some of his cards over to his younger brother, so that justin still has 5 more cards than his brother. how many cards should justin give to his brother? fill in the blanks provided and solve for the answer.

if justin passes \\(x\\) cards to his younger brother,
justins cards \\(\
ightarrow\\) cards
the younger brothers cards \\(\
ightarrow\\) cards

the equation for the number of cards,
justins cards cards = younger brothers cards + difference in the number of cards between brothers cards

solve the above equation.
(ans.) cards

1. scott bought 14 cookies and pamela bought 24 cookies. their teacher asked pamela to give scott some of her cookies, so that he had 2 more cookies than her. how many cookies should pamela give scott?

(ans.) cookies

1. david bought 28 cupcakes and sydney bought 12 cupcakes. david decided to give some of his cupcakes to sydney so that she had 6 more cupcakes than him. how many cupcakes should david give to sydney?

(ans.) cupcakes

Explanation:

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<reasoning>

Set up expressions for Question 1

Using the Difference and Sharing Word Problems and Algebraic Word Problems knowledge points
Let \(x\) be the number of cards Justin passes to his younger brother.

• Justin's remaining cards: \(26 - x\)
• Younger brother's new cards: \(11 + x\)

Formulate and solve the equation for Question 1

Using the Two-Step Equations and One-Step Equations knowledge points
The problem states Justin still has 5 more cards than his brother:
\[
26 - x = (11 + x) + 5
\]
\[
26 - x = 16 + x
\]
\[
2x = 10 \implies x = 5
\]

Solve Question 2

Using the Difference and Sharing Word Problems and Algebraic Word Problems knowledge points
Let \(y\) be the number of cookies Pamela gives to Scott.

• Scott's cookies: \(14 + y\)
• Pamela's cookies: \(24 - y\)

Scott has 2 more cookies than Pamela:
\[
14 + y = (24 - y) + 2
\]
\[
14 + y = 26 - y
\]
\[
2y = 12 \implies y = 6
\]

Solve Question 3

Using the Difference and Sharing Word Problems and Algebraic Word Problems knowledge points
Let \(z\) be the number of cupcakes David gives to Sydney.

• David's cupcakes: \(28 - z\)
• Sydney's cupcakes: \(12 + z\)

Sydney has 6 more cupcakes than David:
\[
12 + z = (28 - z) + 6
\]
\[
12 + z = 34 - z
\]
\[
2z = 22 \implies z = 11
\]
</reasoning>

<answer>

Question 1

If Justin passes \(x\) cards to his younger brother:

• Justin's cards \(\Rightarrow\) \(26 - x\) cards
• The younger brother's cards \(\Rightarrow\) \(11 + x\) cards

The equation for the number of cards:

• Justin's cards: \(26 - x\) cards \(=\) Younger brother's cards + Difference: \(11 + x + 5\) cards

Solve the above equation:

• (Ans.) \(5\) cards

Question 2

• (Ans.) \(6\) cookies

Question 3

• (Ans.) \(11\) cupcakes

</answer>

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Answer:

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<reasoning>

Set up expressions for Question 1

Using the Difference and Sharing Word Problems and Algebraic Word Problems knowledge points
Let \(x\) be the number of cards Justin passes to his younger brother.

• Justin's remaining cards: \(26 - x\)
• Younger brother's new cards: \(11 + x\)

Formulate and solve the equation for Question 1

Using the Two-Step Equations and One-Step Equations knowledge points
The problem states Justin still has 5 more cards than his brother:
\[
26 - x = (11 + x) + 5
\]
\[
26 - x = 16 + x
\]
\[
2x = 10 \implies x = 5
\]

Solve Question 2

Using the Difference and Sharing Word Problems and Algebraic Word Problems knowledge points
Let \(y\) be the number of cookies Pamela gives to Scott.

• Scott's cookies: \(14 + y\)
• Pamela's cookies: \(24 - y\)

Scott has 2 more cookies than Pamela:
\[
14 + y = (24 - y) + 2
\]
\[
14 + y = 26 - y
\]
\[
2y = 12 \implies y = 6
\]

Solve Question 3

Using the Difference and Sharing Word Problems and Algebraic Word Problems knowledge points
Let \(z\) be the number of cupcakes David gives to Sydney.

• David's cupcakes: \(28 - z\)
• Sydney's cupcakes: \(12 + z\)

Sydney has 6 more cupcakes than David:
\[
12 + z = (28 - z) + 6
\]
\[
12 + z = 34 - z
\]
\[
2z = 22 \implies z = 11
\]
</reasoning>

<answer>

Question 1

If Justin passes \(x\) cards to his younger brother:

• Justin's cards \(\Rightarrow\) \(26 - x\) cards
• The younger brother's cards \(\Rightarrow\) \(11 + x\) cards

The equation for the number of cards:

• Justin's cards: \(26 - x\) cards \(=\) Younger brother's cards + Difference: \(11 + x + 5\) cards

Solve the above equation:

• (Ans.) \(5\) cards

Question 2

• (Ans.) \(6\) cookies

Question 3

• (Ans.) \(11\) cupcakes

</answer>

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