Let’s go through each problem one by one.
---
Problem 1:
Mr. Swanson starts with
c students. He picks up
5 new students.
→ So, the new number of students is:
Algebraic Expression: c + 5
Now, if there were originally
27 students, then:
→ Numerical Expression: 27 + 5
→ Answer: 32
✔ Check: 27 + 5 = 32 → Correct.
---
Problem 2:
Pratap has
six times as many coins as Yoshiko. Yoshiko has
y coins.
→ So, Pratap has:
Algebraic Expression: 6y
If Yoshiko has
47 coins, then:
→ Numerical Expression: 6 × 47
→ Let’s calculate: 6 × 40 = 240, 6 × 7 = 42 → 240 + 42 = 282
→ Answer: 282
✔ Check: 6 × 47 = 282 → Correct.
---
Problem 3:
Ayana runs
13 laps less than Emma.
We’re told to pick our own variable for Emma’s laps — let’s use
e for Emma’s laps.
→ So, Ayana’s laps = e - 13
Algebraic Expression: e - 13
If Emma runs
32 laps, then:
→ Numerical Expression: 32 - 13
→ Answer: 19
✔ Check: 32 - 13 = 19 → Correct.
---
Problem 4:
Nicki’s age = quotient of Granny’s age and six → that means divide Granny’s age by 6.
Pick a variable for Granny’s age — let’s use
g.
→
Algebraic Expression: g ÷ 6 or g/6
If Granny is
72 years old, then:
→ Numerical Expression: 72 ÷ 6
→ Answer: 12
✔ Check: 72 ÷ 6 = 12 → Correct.
---
Problem 5:
Number of 8th graders =
2/3 of number of 7th graders.
Pick a variable for 7th graders — let’s use
s.
→
Algebraic Expression: (2/3)s
If there are
96 students in 7th grade, then:
→ Numerical Expression: (2/3) × 96
→ Calculate: 96 ÷ 3 = 32, then 32 × 2 = 64
→ Answer: 64
✔ Check: (2/3) × 96 = 64 → Correct.
---
Final Answer:
1. Algebraic: c + 5; Numerical: 27 + 5; Answer: 32
2. Algebraic: 6y; Numerical: 6 × 47; Answer: 282
3. Algebraic: e - 13; Numerical: 32 - 13; Answer: 19
4. Algebraic: g ÷ 6; Numerical: 72 ÷ 6; Answer: 12
5. Algebraic: (2/3)s; Numerical: (2/3) × 96; Answer: 64
Parent Tip: Review the logic above to help your child master the concept of translating word problems into algebraic expressions worksheet.
