Here's the complete solution to all 8 percentage problems from your worksheet, with clear step-by-step explanations.
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1) Express the following as a percentage.
To convert “X out of Y” to a percentage:
→
(X ÷ Y) × 100%
a)
68 out of 100
= (68 ÷ 100) × 100% =
68%
b)
20 out of 50
= (20 ÷ 50) × 100% = 0.4 × 100% =
40%
c)
54 out of 432
= (54 ÷ 432) × 100% = 0.125 × 100% =
12.5%
✔ Answers: a) 68%, b) 40%, c) 12.5%
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2) Calculate the following:
To find “X% of Y”:
→
(X ÷ 100) × Y
a)
26% of $1500
= (26 ÷ 100) × 1500 = 0.26 × 1500 =
$390
b)
14% of 258ml
= (14 ÷ 100) × 258 = 0.14 × 258 =
36.12 ml
c)
17% of $5500 salary for a bag
= (17 ÷ 100) × 5500 = 0.17 × 5500 =
$935
✔ Answers: a) $390, b) 36.12 ml, c) $935
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3) Percentage of apples in fruit stall
First, find total number of fruits:
- Pears: 29
- Watermelons: 7
- Papayas: 12
- Oranges: 27
- Apples: 25
Total fruits = 29 + 7 + 12 + 27 + 25 = 100
Apples = 25
Percentage of apples = (25 ÷ 100) × 100% =
25%
✔ Answer: 25%
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4) Number of children at carnival
Given: 45% are adults → so
55% are children (since 100% - 45% = 55%)
Also given: 135 adults → this is 45% of total people.
Let total people = T
Then:
45% of T = 135
→ 0.45T = 135
→ T = 135 ÷ 0.45 =
300
Children = 55% of 300 = 0.55 × 300 =
165
✔ Answer: 165 children
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5) Total payment at Hannah Restaurant
Meal cost = $29
Service charge = 10% of $29 = 0.10 × 29 = $2.90
GST = 7% of $29 = 0.07 × 29 = $2.03
Total = Meal + Service + GST
= 29 + 2.90 + 2.03 =
$33.93
✔ Answer: $33.93
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6) Joseph’s total payment after 15% discount
Jeans = $68
Shirt = $39
Total before discount = 68 + 39 =
$107
Discount = 15% of $107 = 0.15 × 107 = $16.05
Amount to pay = 107 - 16.05 =
$90.95
✔ Answer: $90.95
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7) Original price of dress before 20% discount
Grace spent 2/11 of her salary on the dress and had $1008 left.
That means the
remaining 9/11 of her salary = $1008
Let total salary = S
Then:
(9/11)S = 1008
→ S = 1008 × (11/9) = 112 × 11 =
$1232
She spent 2/11 of salary on the dress:
→ (2/11) × 1232 = 2 × 112 =
$224
This $224 is the
discounted price (after 20% off).
Let original price = P
After 20% discount, she paid 80% of P → 0.8P = 224
→ P = 224 ÷ 0.8 =
$280
✔ Answer: $280
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8) Total students in John’s school
Let total students = T
Boys = 68% of T → 0.68T
Girls = 32% of T → 0.32T (since 100% - 68% = 32%)
Given: Boys = Girls + 180
→ 0.68T = 0.32T + 180
Subtract 0.32T from both sides:
0.36T = 180
→ T = 180 ÷ 0.36 =
500
✔ Answer: 500 students
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✔ Final Answers Summary:
1. a) 68% b) 40% c) 12.5%
2. a) $390 b) 36.12 ml c) $935
3. 25%
4. 165 children
5. $33.93
6. $90.95
7. $280
8. 500 students
Let me know if you’d like these formatted as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of percentage worksheet grade 7.
