write an inequalityand solve the equation

Question

your grandmother gave you a $500 gift card. You want to buy as many video games as possible. Each game is $45.99 each. You will be charged a flat rate of $12.99 shipping . how many video games can you buy?

Answer 1

Dear Heather, Inequalities can be tricky. Just stop and think them through. Put yourself in an online store and think about the math boundaries of your situation.

 

• you can't spend more than $500 with just the card alone.
• each video game has the same price, $45.99.
• a flat shipping rate means you are charged one price for as many games as you purchase.

 

This is a basic linear equation converted to an inequality, so let's look at a word equation to start with:

 

price of each game x number purchased + flat shipping rate <= or >= card balance

 

Can you spend more than what is on the card?  No, what you spend has to be less than the balance.

 

price of each game x number purchased + flat shipping rate <=  card balance

 

$45.99 x n + $12.99 <=$500        Substitute the values; let n be the unknown number of games bought.

                  - $12.99    -$12.99      Just as if it was an equation, subtract the constant from both sides.

 

$45.99n <= $487.01

 

$45.99n  / $45.99<= $487.01/$45.99  Divide both sides to get just a single n.

 

n <= 10.589                                  The answer is rounded to 3 decimal places.

                                                     But you can't stop here. Can you really buy .589 of a game? No

 

n <= 10  Final answer.                 You can only buy whole games, so drop the decimal part.

 

Check:

$45.99(10) + 12.99 <= $500 ?        Plug in.  

$459.90 + 12.99 <= $500 ?             

$472.89 <= $500                            True value. But it would be true for 9, 8, or 3 games purchased.

                                                          You need to check if there's enough left on the card to buy another game.

$500-$472.89 = $27.11 < $45.99     True, again, but now we know 10 is the most games you could buy.

 

But you have to read between the lines on the question: "how many video games can you buy?" They might mean the most, 10 games. But based upon how the question is exactly worded, the best answer would be: "I could buy no more than 10 video games with grandma's gift card." (This answer would really impress your math teacher. It's also the way we really answer questions on the job, outside of the classroom.)