Question

pattern 6 - increase and decrease
brenda has 41 marbles and her younger sister has 13 marbles.
their mother asked brenda to give her sister some of her marbles, so that she has 10 more marbles than her sister.
how many marbles should brenda give to her sister?

try! - fill in the blanks provided and solve for the answer.

(1) if brenda passes \\(x\\) marbles to her younger sister,
brendas marbles \\(\
ightarrow\\) initial pieces - pieces passed pieces
the younger sisters marbles \\(\
ightarrow\\) initial pieces + pieces received pieces

(2) find the equation for number of marbles.
brendas marbles pieces = younger sisters marbles pieces + difference of pieces between brendas and younger sisters pieces

solve the above equation.

Explanation:

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<reasoning>

Represent the marble counts algebraically

Using the One-Step Equations knowledge point, we express the number of marbles each sister has after Brenda gives \(x\) marbles to her younger sister.
Brenda starts with 41 marbles and gives away \(x\):
\[41 - x\]
The younger sister starts with 13 marbles and receives \(x\):
\[13 + x\]

Set up the equation

The problem states Brenda should have 10 more marbles than her sister.
\[\text{Brenda's marbles} = \text{Younger sister's marbles} + 10\]
Substituting the algebraic expressions:
\[41 - x = (13 + x) + 10\]

Solve the equation for x

Simplify the right side of the equation:
\[41 - x = 23 + x\]
Add \(x\) to both sides:
\[41 = 23 + 2x\]
Subtract 23 from both sides:
\[18 = 2x\]
Divide by 2:
\[x = 9\]
</reasoning>

<answer>

Question 1

(1) If Brenda passes \(x\) marbles to her younger sister,

Brenda's marbles \(\Rightarrow\) <blank>41</blank> \(-\) <blank>\(x\)</blank> pieces

The younger sister's marbles \(\Rightarrow\) <blank>13</blank> \(+\) <blank>\(x\)</blank> pieces

Question 2

(2) Find the equation for number of marbles.

<blank>\(41 - x\)</blank> pieces \(=\) <blank>\(13 + x\)</blank> pieces \(+\) <blank>10</blank> pieces

Solve the above equation.
\[

$$\begin{aligned} 41 - x &= 13 + x + 10 \\ 41 - x &= 23 + x \\ 2x &= 18 \\ x &= 9 \end{aligned}$$

\]

(Ans.) <blank>9</blank> marbles
</answer>

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Answer:

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<reasoning>

Represent the marble counts algebraically

Using the One-Step Equations knowledge point, we express the number of marbles each sister has after Brenda gives \(x\) marbles to her younger sister.
Brenda starts with 41 marbles and gives away \(x\):
\[41 - x\]
The younger sister starts with 13 marbles and receives \(x\):
\[13 + x\]

Set up the equation

The problem states Brenda should have 10 more marbles than her sister.
\[\text{Brenda's marbles} = \text{Younger sister's marbles} + 10\]
Substituting the algebraic expressions:
\[41 - x = (13 + x) + 10\]

Solve the equation for x

Simplify the right side of the equation:
\[41 - x = 23 + x\]
Add \(x\) to both sides:
\[41 = 23 + 2x\]
Subtract 23 from both sides:
\[18 = 2x\]
Divide by 2:
\[x = 9\]
</reasoning>

<answer>

Question 1

(1) If Brenda passes \(x\) marbles to her younger sister,

Brenda's marbles \(\Rightarrow\) <blank>41</blank> \(-\) <blank>\(x\)</blank> pieces

The younger sister's marbles \(\Rightarrow\) <blank>13</blank> \(+\) <blank>\(x\)</blank> pieces

Question 2

(2) Find the equation for number of marbles.

<blank>\(41 - x\)</blank> pieces \(=\) <blank>\(13 + x\)</blank> pieces \(+\) <blank>10</blank> pieces

Solve the above equation.
\[

$$\begin{aligned} 41 - x &= 13 + x + 10 \\ 41 - x &= 23 + x \\ 2x &= 18 \\ x &= 9 \end{aligned}$$

\]

(Ans.) <blank>9</blank> marbles
</answer>

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