Question

In March, Arnold finds a guitar with a price of $650 that he wants to buy, but he only has $300 dollars saved. In September, Arnold has 75% more money saved, and the guitar is on sale for a 30% discount off of the original price. The sales tax is 5% of the sale price. Does Arnold have enough money to buy the guitar in September? Justify you answer in 2-3 sentences

Answer 1

Since Arnold has 75% more money saved, then he has 175% of the money he had in March. This is equal to:

`\text{money}_{\text{september}}=300\cdot(175)/(100)=525`

He has $525 saved.

The guitar is on sale for a discount of 30%, so the new price is 70% of what it used to be. The new price is:

`\text{guitar}_{}=650\cdot(70)/(100)=455`

But he also needs to pay the sales tax of 5%, which will make the total paid equal to 105% after the discount. We have:

`\text{ final price=455}\cdot(105)/(100)=477.75`

Since the amount of money Arnold has saved is greater than the price of the guitar after the disccount and tax, he has enough money to buy it.