Question

The cost of three notebooks and four pencils is $8.50 the cost of five notebooks and eight pencils is $14.50. Determine the cost of one notebook and the cost of one pencil

Answer 1

looking

Explanation:

Call the notebooks x, and the pencils y.

3x + 4y = $8.50 and 5x + 8y = $14.50

Then just solve as simultaneous equations: 3x + 4y = $8.50

5x+8y = $14.50

5(3x+4y = 8.5) 3(5x + 8y = 14.5)

15x+20y= 42.5 15x + 24y = 43.5

Think: DASS (Different Add, Similar

Subtract). 15x appears in both equations

so subtract one equation from the other. Eassier to subtract (15x + 20y = 42.5) from (15x + 24y = 43.5)

(15x + 24y = 43.5) - (15x + 20y= 42.5) = (4y = 1) which means y = 0.25.

Then substitue into equation:

15x+20y=42.5

15x+5+ 42.5

15x=42.5 -5=37.5

15x = 37.5

x = 2.5

15x + 24y = 43.5

15(2.5) + 24(0.25) 37.5+6=43.5

So x (notebooks) are 2.5 ($2.50) each and y (pencils) are 0.25 ($0.25) each.