Linear Inequality (Introduction)

posted by Mr Johari

Introduction to Linear Inequalities

Suppose you have a gift card for $100 to an electronics store and want to spend it on CDs and DVDs. You want a special-edition DVD that costs $24.99, and the CDs you want are all on sale for $11.99 each. Assuming that you use only the gift card and you are going to buy the DVD, what is the maximum number of CDs you can buy?

You know you can buy at least one CD. What about two CDs? It can be time consuming to keep checking.

Post ways to solve this problem.

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  1. change all the approximations to whole numbers, $24.99 to $25,and $11.99 to $12, so we take $100-$25,divided by 12,which gets about 6.

  2. 100-24.99=75.01------>the amount of $$ left after buying DVD
    75.01/11.99=6.25...->round off -> 6

    "I" can buy 1 DVD and 6 CDs

  3. by rounding all the values to the nearest whole number, it is...

    Special edition DVD = $24.99
    ≈ $25
    CD = $11.99
    ≈ $ 12

    So taking $100 - $25 for the DVD,

    the leftover money will be $75.
    So for the CDs...
    $75 ÷ $12 = 6 R$3

    We do not want to exceed the money from the gift voucher, so we take the quotient [ ? not sure if it's the correct term.. please correct me if it isn't :) ] which is 6.

    So with $100, we can buy: 1 Special Edition DVD and 6 CDs without exceeding the money given.