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Question 1
At the St. George's College bookshop, pens are sold at x dollars and rulers at
y dollars each. A student bought 4 pens and 5 rulers for $24 on Monday. He
then went back on Tuesday and bought 2 of the same pens and 7 of the same
rulers for $21.
i.
ii.
Write two equations in x and y to represent the information given above.
[2 marks]
Solve the equations for x and y.
[4 marks]
Calculate the total cost for one pen and one ruler.
ni.

Respuesta :

MrRoyal

The cost of one pen is $3.5 and one ruler is $2

Represent pen with x, and rulers with y.

So, the equations are:

  • [tex]4x + 5y = 24[/tex] -- on Monday
  • [tex]2x + 7y = 21[/tex]  -- on Tuesday

To solve for x and y, we start by multiplying the second equation by 2

[tex]2(2x + 7y = 21)[/tex]

[tex]4x + 14y = 42[/tex]

Subtract [tex]4x + 5y = 24[/tex] from [tex]4x + 14y = 42[/tex]

[tex]4x - 4x + 14y - 5y = 42 - 24[/tex]

Simplify the expression

[tex]9y = 18[/tex]

Divide both sides by 9

[tex]y = 2[/tex]

Substitute 2 for y in [tex]2x + 7y = 21[/tex]

[tex]2x + 7(2) = 21[/tex]

This gives

[tex]2x + 14 = 21[/tex]

Collect like terms

[tex]2x = 21 -14[/tex]

Evaluate like terms

[tex]2x = 7[/tex]

Divide both sides by 2

[tex]x = 3.5[/tex]

Hence, the cost of one pen is $3.5 and one ruler is $2

Read more about system of equations at:

https://brainly.com/question/14323743