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Tina spent a total of $14.90 on 4 identical notebooks and 3 identical pencils. She
had some money left. If she bought another identical pencil, she would have $0.30
left. If she bought another identical notebook instead, she will be short of $1.50.

How much more does a notebook cost than a pencil?

Respuesta :

$14.90 spent with the amount left for an extra pencil or notebook being $0.30 or $1.50 short respectively indicates that a notebook costs $1.8 more than a pencil.

Which method can be used to calculate the difference in costs?

Let x represent the cost of a notebook and let y represent the cost of a pencil. The following equations can be obtained;

4•x + 3•y = 14.9...(1)

Let a represent the total money Tina has, which gives;

4•x + 4•y = a - 0.3...(2)

5•x + 3•y = a + 1.5...(3)

Subtracting equation (2) from equation (3) gives;

5•x - 4•x + 3•y - 4•y = a - a + 1.5 - (-0.3) = 1.8

Which gives;

  • x - y = 1.8...(4)

  • From the above, we have that the difference between the cost of a notebook and pencil is 1.8

Multiplying equation (4) by 4 and subtracting the result to equation (1) gives;

4 × (x - y) = 4 × 1.8 = 7.2

4•x - 4•y = 7.2

4•x - 4•x + 3•y - (-4•y) = 14.9 - 7.2 = 7.7

7•y = 7.7

  • y = 7.7 ÷ 7 = 1.1

  • The cost of a pencil, y = $1.1

x - y = 1.8

x = 1.8 + 1.1 = 2.9

  • Cost of a notebook, x = $2.9

The difference between the cost of a notebook and the cost of a pencil is therefore;

x - y = $2.9 - $1.1 = $1.8

  • A notebook costs $1.8 more than a pencil.

Learn more about writing equations here:

https://brainly.com/question/776122

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