Question

how can you use an equation to find an unknown value in a proportional relationship in an 7th graders words

Answer 1

Here’s a simple way to explain it for a 7th grader.

1) What “proportional” means
- Two quantities are proportional when they change by the same factor.
- That means their ratio (one divided by the other) is always the same number. Example: if 2 pencils cost $1, then 4 pencils cost $2, because the cost per pencil (ratio) is the same.

2) Two easy ways to find the unknown

Method A — Use a unit rate (what one costs/is)
- Find the value for one unit (divide).
Example: 6 cookies cost $3. How much do 10 cookies cost?
First find cost for 1 cookie: 3 ÷ 6 = $0.50.
Then multiply by 10: 0.50 × 10 = $5.
So 10 cookies cost $5.

Method B — Use an equation and cross-multiply (good when you set up a fraction)
- Set up a proportion as two equal fractions: known1 / known2 = unknown1 / unknown2.
Example: 3 notebooks cost $9. How much do 8 notebooks cost? Let x = cost for 8.
Write: 3/9 = 8/x (notebooks/cost on each side)
Cross-multiply: 3·x = 9·8
So 3x = 72. Divide both sides by 3: x = 24.
The 8 notebooks cost $24.

3) Another common form: y = kx
- Here k is the constant of proportionality (the unit rate). If y and x are proportional, y = kx.
Example: If 5 pens cost $2, then k = 2/5 = $0.40 per pen. For 12 pens, y = 0.4 × 12 = $4.80.

4) Quick check
- After you get an answer, check the ratio is the same as the original ratio.

Practice problem: 7 apples cost $2.10. How much do 15 apples cost?
- Unit rate: 2.10 ÷ 7 = $0.30 per apple.
- Multiply: 0.30 × 15 = $4.50. So 15 apples cost $4.50.

That’s it — either find the unit rate and multiply, or set up a proportion and solve for the unknown with cross-multiplication.