algebra

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A coffee shop sells small cups of coffee and large cups of coffee.

A small cup of coffee costs $2.
A large cup of coffee costs $3.
On Tuesday, the store sold a total of 155 cups of coffee for a total of $335.
How many small cups of coffee did the store sell on Tuesday?

  • algebra -

    Conventional algebra:
    x=number of small cups
    y=number of large cups
    form the system of equations
    x+y=155
    2x+3y=335
    Solve the system for x and y.

    Quick way by substituting directly:
    Let 155-x=number of large cups
    2x+3(155-x)=335
    Solve the linear equation for x.

    Faster way by mental calculations:
    Assume all sold are small,
    then proceeds
    =2x155=310

    Money left-over = $335-310 = 25
    Exchange 25 small cups for 25 large cups for $25, so
    small cups = 155-25=130
    large cups = 25.

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