We are given a 7th-grade math review worksheet with
6 proportions to solve. Below each proportion is a box where we must write the solution. At the bottom, there’s an “Answer Bank” with numbers:
2, 5, 21, 36, 52, 78, 80, 84, 108 — and it says *“Not all answers will be used!”*
---
Let’s solve each proportion one by one using
cross-multiplication.
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#1: x/6 = 13/39
Cross-multiply:
> x × 39 = 6 × 13
> 39x = 78
> x = 78 ÷ 39
>
x = 2
✔ Answer:
2
---
#2: 7/x = 4/12
Cross-multiply:
> 7 × 12 = 4 × x
> 84 = 4x
> x = 84 ÷ 4
>
x = 21
✔ Answer:
21
---
#3: 24/36 = x/54
Cross-multiply:
> 24 × 54 = 36 × x
> Let’s compute 24×54:
> 24 × 50 = 1200, 24 × 4 = 96 → total = 1296
> So: 1296 = 36x
> x = 1296 ÷ 36
> Let’s divide: 36 × 36 = 1296 → so
>
x = 36
✔ Answer:
36
*(Note: You could also simplify 24/36 = 2/3, then 2/3 = x/54 → x = (2/3)×54 = 36)*
---
#4: 15/27 = 60/x
Cross-multiply:
> 15 × x = 27 × 60
> 15x = 1620
> x = 1620 ÷ 15
> 15 × 108 = 1620 → so
>
x = 108
✔ Answer:
108
*(Alternatively: 15/27 simplifies to 5/9 → 5/9 = 60/x → cross-multiply: 5x = 540 → x=108)*
---
#5: 76/x = 19/20
Cross-multiply:
> 76 × 20 = 19 × x
> 1520 = 19x
> x = 1520 ÷ 19
> 19 × 80 = 1520 → so
>
x = 80
✔ Answer:
80
---
#6: x/78 = 30/45
First, simplify 30/45 → divide numerator and denominator by 15 → 2/3
So: x/78 = 2/3
Cross-multiply:
> x × 3 = 78 × 2
> 3x = 156
> x = 156 ÷ 3
>
x = 52
✔ Answer:
52
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##
✔ Final Answers:
| Problem | Answer |
|---------|--------|
| #1 | 2 |
| #2 | 21 |
| #3 | 36 |
| #4 | 108 |
| #5 | 80 |
| #6 | 52 |
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## 🟩 Used from Answer Bank:
2, 21, 36, 52, 80, 108
##
✘ Not Used:
5, 78, 84
*(As stated: “Not all answers will be used!” — correct!)*
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✔ All problems solved correctly using cross-multiplication and simplification where helpful.
Parent Tip: Review the logic above to help your child master the concept of math worksheet 7th grade.
