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anonymous

  • one year ago

A charity organisation sells greetings cards in packs costing $10 or $2.50 each. A total of 75 packs were sold at a fair for a total of $375. How many of the $2.50 packs were sold?

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  1. mathstudent55
    • one year ago
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    This problem can solved with a system of equations. First, we need two variables to represent the two unknown numbers. Let x = the number of $10 packs. Let y = the number of $2.50 packs.

  2. mathstudent55
    • one year ago
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    We are told that 75 packs were sold. Using our two variables, we know the number of packs sold is \(x + y\) This gives us our first equation: \(x + y = 75\) Do you follow so far?

  3. anonymous
    • one year ago
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    yes I struggle when it comes to find the y

  4. anonymous
    • one year ago
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    You'll have a second equation: 10x + 2.5y = 375

  5. anonymous
    • one year ago
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    $10 for x packs, $2.50 for the y packs. Hopefully that makes sense.

  6. mathstudent55
    • one year ago
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    Wait. We only wrote one equation so far. The equation we wrote has two variables. To find the values of two variables, we need two equations. That equation dealt with the number of packs. Now we need an equation that deals with the amount of money.

  7. anonymous
    • one year ago
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    375 is the amount of money that was received in the end.

  8. mathstudent55
    • one year ago
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    If x number of $10 packs were sold, that was 10x dollars. If y number of $2.50 packs were sold, that was 2.5y dollars. We add the two amounts and we get 10x + 2.5y We are told that $375 was the total amount of dollars sold, so that gives us the second equation \(10x + 2.5y = 375\)

  9. mathstudent55
    • one year ago
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    Now we have two equations in two unknowns. We can find the values of the variables.

  10. mathstudent55
    • one year ago
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    This is the system of equations we need to solve to find the value of y, the number of $2.50 packs that were sold. \(\begin{cases} x + y = 75 \\ 10x + 2.5y = 375 \end{cases}\)

  11. anonymous
    • one year ago
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    I follow you! I was getting there but I can't understand the way it is solved after having these 2 equations. I can go as far as 10x=750-10y but then I dont know what to do with the 750 ty

  12. mathstudent55
    • one year ago
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    We are solving for y, the number of $2.50 packs because that is all the problem asks for. Let's solve the system by substitution. We solve the first equation for x. \(x = 75 - y\) Now we replace x of the second equation with \(\color{red}{75 - y}\). \(10\color{red}{x} + 2.5y = 375\) \(10\color{red}{(75 - y)} + 2.5y = 375\) Distribute the 10. \(750 - 10y + 2.5y = 375\) Combine like terms on the left side. \(750 - 7.5 y = 375\) Subtract 750 from both sides. \(-7.5y = -375\) Divide both sides by -7.5 \(y = 50\) Since y represents the number of $2.50 packs, the answer is: The number of $2.50 packs sold is 50.

  13. anonymous
    • one year ago
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    God, only a misread of negativ...thanks so much for helping!

  14. mathstudent55
    • one year ago
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    You're welcome.

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