9 A 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.

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.

rounding to the nearest thousandth would be 452,000

step-by-step explanation:

answers available in this download

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