Build and solve factorisable quadratic models, then interpret their solutions.
Free examples and worked answers. No account needed.
Practise the method.
Build and solve factorisable quadratic models, then interpret their solutions.
Build and solve factorisable quadratic models, then interpret their solutions.
Example 1
A stall sells (11+x) items at ($21−x) each and pays a fixed $2 cost. For which two whole-number values of x is its profit $253?
Show worked answer
Answer: x=4x=6
Profit is (11+x)(21−x)−2.
Equate it to 253 and rearrange: x2−10x+24=0=(x−4)(x−6).
Both 4 and 6 give positive prices and item counts.
Example 2
A rectangular garden is 7m longer than it is wide. A path 3m wide surrounds all four sides. Garden and path together cover 170m2. Find the perimeter of the garden itself.
Garden and surrounding pathDiagram not to scaleShow worked answer
Answer: 30
Let garden width be x.
The outside dimensions are x+6 and x+13.
Solve their product =170;
the positive solution is x=4.
Garden length is 11
its perimeter is 2(4+11)=30m.
Example 3
A stall sells (9+x) items at ($17−x) each and pays a fixed $2 cost. For which two whole-number values of x is its profit $158?
Show worked answer
Answer: x=1x=7
Profit is (9+x)(17−x)−2.
Equate it to 158 and rearrange: x2−8x+7=0=(x−1)(x−7).
Both 1 and 7 give positive prices and item counts.
Put it into practice.
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