1.7 Modeling with Equations
Ideas in this lesson
- Expressing quantities with a variable
- Money, costs and averages
- Interest and investments
- Geometry and dimensions
- Mixture and concentration
- Work problems
- Distance, rate and time
- Number, consecutive-integer and age problems
- Solid geometry and balance
- Linked geometry, paths and model communication
Expressing quantities with a variable · Worked example
A rectangle has width x meters and length 3 meters more than 5 times its width. Which area model and physical domain are correct?
Answer: \(A=x(5x+3)\) square meters; \(x>0\)
The phrase “5 times its width” gives \(5x\).
Adding \(3\) meters gives length \(5x+3\).
Area is width times length, rather than twice the sum.
A physical rectangle needs positive width; this also makes its stated length positive.
Adding \(3\) meters gives length \(5x+3\).
Area is width times length, rather than twice the sum.
A physical rectangle needs positive width; this also makes its stated length positive.