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11 September, 16:12

A teacher is buying supplies for an upcoming art project. She buys x bottles of paint for $1.29 each. She buys 8 more canvases than bottles of

paint for $1.89 each. Her total pretax cost is $37.38. How many of each item is she buying?

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  1. 11 September, 16:17
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    She is buying 7 bottles and 15 canvases of paint

    Step-by-step explanation:

    * Lets change the story problem to equations and solve them

    - The teacher buys x bottles of paint for $1.29 each

    - She buys 8 more canvases than bottles of paint for $1.89 each

    - Her total pretax cost is $37.38

    * Lets write an equation represented these information

    ∵ x is the number of the bottles of paint

    ∵ She buys 8 more canvases than bottles

    ∴ The number of canvases of paint = x + 8

    ∵ Her total pretax is $37.38

    ∵ The cost of a bottle of paint is $1.29

    ∵ The cost of a canvas of paint is $1.89

    ∴ 1.29 (x) + 1.89 (x + 8) = 37.38

    - Simplify the equation

    ∴ 1.29 x + 1.89 x + 15.12 = 37.38

    ∴ 3.18 x + 15.12 = 37.38

    - Subtract 15.12 from both sides

    ∴ 3.18 x = 22.26

    - Divide both sides by 3.18

    ∴ x = 7

    ∵ x represents the number of bottles

    ∴ The number of bottles of paint is 7

    ∵ x + 8 represents the number of canvases

    ∴ The number of canvases = 7 + 8 = 15

    ∴ The number of canvases of paint is 15

    ∴ She is buying 7 bottles and 15 canvases of paint
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