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RV-21-001 · Simultaneous equations from bundles and a discount

A stationery shop sells folders and pens. 4 folders and 5 pens cost £67. 5 folders and 5 pens cost £80. A customer buys 5 folders and 4 pens and receives a 10% discount on the whole purchase. Work out the amount paid.

Simultaneous Equations in Context with Percentage Discount Booklet p. 27 & p. 51
Method
1) Label both equations
2) Make the first-letter coefficients equal
3) Subtract the entire second equation, watching touching signs
4) Solve for the second letter
5) Substitute back to find the first
Worked Example (RV-21-001)
1)
Let x be the folder price and y the pen price, in pounds.
2)
Label the equations: 4x+5y=67(1)4x + 5y=67\quad(1) and 5x+5y=80(2)5x + 5y=80\quad(2).
3)
Match the first-letter coefficients: (1) × 5, (2) × 4.
4)
20x+25y=33520x+20y=320(25−(20))y=335−(320)\begin{array}{rcl}20x + 25y&=&335\\ 20x + 20y&=&320\\\hline (25-(20))y&=&335-(320)\end{array}
5)
Subtract the entire second equation, including its signs: 5y=15⇒y=35y=15\Rightarrow y=3.
6)
Substitute into (1): 4x+(5)(3)=67⇒4x=52⇒x=134x+(5)(3)=67\Rightarrow 4x=52\Rightarrow x=13.
7)
Before discount: 5(13)+4(3)=775(13)+4(3)=77 pounds.
8)
Amount paid: 77×0.9=69.3077\times0.9=69.30 pounds.
Ans = £69.30