shop sells pens and notebooks. The cost of a pen is p cents and the cost of a notebook is n cents. (a) On Monday, the shop sells 5 pens and 4 notebooks for 450 cents. Complete the equation. 5p + 4n = (b) On Tuesday, the shop sells 10 pens and 3 notebooks for 525 cents. Write this information as an equation. (c) Solve your two equations to find the cost of a pen and the cost of a notebook. You must show all your working.
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Answer:
Answer: n = 75; p = 30
Explanation: (a) 5p + 4n = 450 where p is for pen and n is for notebook.
(b) 10p + 3n = 525
We can use the elimination method to solve these two equations.
1. Multiply the first equation by 2 so that 10p will cancel out:
2(5p + 4n = 450)
- 10p + 3p = 525
10p + 8n = 900
- 10 p + 3n = 525
5n = 375
2. Divide by 5 to get n alone: n = 75
3. Plug 75 into the first equation: 5p + 4(75) = 450
5p + 300 = 450
4. Subtract 300 from 450: 5p = 150
5. Divide by 5 to get p alone: p = 30
We can test if this is correct by plugging our answers into the second equation:
10(30) + 3(75) = 525
300 + 225 = 525
525 = 525
This is a true statement, which means that our answers are correct.
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