SME
Grade 11 Math · Problem type
Inverse variation
Use this for “6 workers take 10 days. How long do 4 workers take?”
Chart
Vertical asymptote x₂ = 0
Horizontal asymptote y = 0
f(4) = 15
First x: 6
First y: 10
This is an example. Type your own values to start a new problem.
x₁
×
y₁
=
k
=
x₂
×
y₂
Formulas
k
=
x₁
×
y₁
60 = 6 × 10
y₂
=
k
x₂
15
=
60
4
Assumptions
•
y varies inversely with x when y = k ÷ x: the product xy is the same constant k.
•
Doubling x halves y.
Step-by-step
WE KNOW
x₁ = 6, y₁ = 10, x₂ = 4
FIND
constant of variation (k), second y (y₂)
Step 1 · Find constant of variation (k)
Use k = x₁ × y₁
The product xy is the same for every pair.
k
=
6
×
10
k
=
60
Step 2 · Find second y (y₂)
Use y₂ = k ÷ x₂
Divide
k
by
the
new
x.
y₂
=
60
4
y₂
=
15
Check
Put the numbers back in. Both sides should match.
60 = 6 × 10 ✓
15
=
60
4
✓
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