Constraints Math Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardA recipe needs at least 2 cups of flour and no more than 5 cups total of flour and sugar combined. If you use 3 cups of flour, what is the range of sugar cups?
Solution
- 1 Flour \(f = 3\) cups (satisfies \(f \geq 2\) ✓).
- 2 Total constraint: \(f + s \leq 5\), so \(3 + s \leq 5\), giving \(s \leq 2\).
- 3 Also \(s \geq 0\) (non-negative).
- 4 Sugar range: \(0 \leq s \leq 2\) cups.
Answer
\(0 \leq s \leq 2\) cups of sugar
Substituting \(f=3\) into the constraint \(f+s \leq 5\) gives \(s \leq 2\). Combined with \(s \geq 0\): \(0 \leq s \leq 2\).
About Constraints
Conditions or restrictions that limit which values are allowed in a problem. Constraints narrow the set of possible solutions, such as 'x must be positive' or 'the total cannot exceed 100.'
Learn more about Constraints →More Constraints Examples
Example 1 medium
You have [formula]3 each) and pens ($2 each). Write the constraint inequality and find a valid combi
Example 2 hardA farmer plants corn ([formula]150/acre profit) on at most 100 acres, with at least 20 acres of corn
Example 3 mediumA box must hold at least 10 items but no more than 25 items. Write this as a compound inequality and