Question

7 jack increased his donations by 11%. this is equal to multiplying that amount by:
a 11%
b 110%
c 1.11
d 1.1

8 jill multiplied her donations by 0.86. this is equal to a percentage change of a:
a 24% decrease
b 14% decrease
c 14% increase
d 24% increase

9 what is the percentage increase if the original price is $50 & the new price is $60?
a $10
b 10%
c 20%
d $20

10 jenny has 1250 photos stored on her mobile. she wants to print 20% of these. if her photos cost 9 cents a photo to print, how much will this printing cost?
a $2250
b $22.50
c $250
d $112.50

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 4,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Percentage Change",
"Decimal Multipliers",
"Percentage Calculations"
],
"current_concepts": [
"Percentage Change",
"Decimal Multipliers",
"Percentage Calculations"
]
}
</pre_analysis>

<reasoning>

Solve Question 7

Find the multiplier for an \(11\%\) increase.
An increase of \(11\%\) means:
\[
100\% + 11\% = 111\%
\]
Convert this percentage to a decimal:
\[
\frac{111}{100} = 1.11
\]
This matches option C.

Solve Question 8

Find the percentage change for a multiplier of \(0.86\).
A multiplier less than \(1\) represents a decrease:
\[
1 - 0.86 = 0.14
\]
Convert the decimal difference to a percentage:
\[
0.14 \times 100\% = 14\% \text{ decrease}
\]
This matches option B.

Solve Question 9

Calculate the percentage increase from \(\$50\) to \(\$60\).
Find the absolute increase:
\[
60 - 50 = 10
\]
Calculate the percentage relative to the original price:
\[
\frac{10}{50} \times 100\% = 20\%
\]
This matches option C.

Solve Question 10

Calculate the total printing cost.
First, find \(20\%\) of the \(1250\) photos:
\[
1250 \times 0.20 = 250 \text{ photos}
\]
Multiply the number of photos by the cost per photo (\(9\) cents or \(\$0.09\)):
\[
250 \times 0.09 = 22.50
\]
The total cost is \(\$22.50\). This matches option B.
</reasoning>

<answer>

Question 7

<mcq-option>A 11%</mcq-option>
<mcq-option>B 110%</mcq-option>
<mcq-correct>C 1.11</mcq-correct>
<mcq-option>D 1.1</mcq-option>

Question 8

<mcq-option>A 24% decrease</mcq-option>
<mcq-correct>B 14% decrease</mcq-correct>
<mcq-option>C 14% increase</mcq-option>
<mcq-option>D 24% increase</mcq-option>

Question 9

<mcq-option>A $10</mcq-option>
<mcq-option>B 10%</mcq-option>
<mcq-correct>C 20%</mcq-correct>
<mcq-option>D $20</mcq-option>

Question 10

<mcq-option>A $2250</mcq-option>
<mcq-correct>B $22.50</mcq-correct>
<mcq-option>C $250</mcq-option>
<mcq-option>D $112.50</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Arithmetic",
"Percentages"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 4,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Percentage Change",
"Decimal Multipliers",
"Percentage Calculations"
],
"current_concepts": [
"Percentage Change",
"Decimal Multipliers",
"Percentage Calculations"
]
}
</pre_analysis>

<reasoning>

Solve Question 7

Find the multiplier for an \(11\%\) increase.
An increase of \(11\%\) means:
\[
100\% + 11\% = 111\%
\]
Convert this percentage to a decimal:
\[
\frac{111}{100} = 1.11
\]
This matches option C.

Solve Question 8

Find the percentage change for a multiplier of \(0.86\).
A multiplier less than \(1\) represents a decrease:
\[
1 - 0.86 = 0.14
\]
Convert the decimal difference to a percentage:
\[
0.14 \times 100\% = 14\% \text{ decrease}
\]
This matches option B.

Solve Question 9

Calculate the percentage increase from \(\$50\) to \(\$60\).
Find the absolute increase:
\[
60 - 50 = 10
\]
Calculate the percentage relative to the original price:
\[
\frac{10}{50} \times 100\% = 20\%
\]
This matches option C.

Solve Question 10

Calculate the total printing cost.
First, find \(20\%\) of the \(1250\) photos:
\[
1250 \times 0.20 = 250 \text{ photos}
\]
Multiply the number of photos by the cost per photo (\(9\) cents or \(\$0.09\)):
\[
250 \times 0.09 = 22.50
\]
The total cost is \(\$22.50\). This matches option B.
</reasoning>

<answer>

Question 7

<mcq-option>A 11%</mcq-option>
<mcq-option>B 110%</mcq-option>
<mcq-correct>C 1.11</mcq-correct>
<mcq-option>D 1.1</mcq-option>

Question 8

<mcq-option>A 24% decrease</mcq-option>
<mcq-correct>B 14% decrease</mcq-correct>
<mcq-option>C 14% increase</mcq-option>
<mcq-option>D 24% increase</mcq-option>

Question 9

<mcq-option>A $10</mcq-option>
<mcq-option>B 10%</mcq-option>
<mcq-correct>C 20%</mcq-correct>
<mcq-option>D $20</mcq-option>

Question 10

<mcq-option>A $2250</mcq-option>
<mcq-correct>B $22.50</mcq-correct>
<mcq-option>C $250</mcq-option>
<mcq-option>D $112.50</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Arithmetic",
"Percentages"
]
}
</post_analysis>