Question

In March, Arnold finds a guitar with a price of $\$650$ that he wants to buy, but he only has $\$300$ saved.

In September, Arnold has $75\%$ more money saved, and the guitar is on sale for a $30\%$ discount off the original price. The sales tax is $5\%$ of the sale price.

Does Arnold have enough money to buy the guitar in September? Justify your answer.

Respond in the space provided.

Answer 1

Arnold has saved $75%$ more money than $$300$ in September, which is equal to $(1+\frac{75}{100})\cdot $300 = $525$. Therefore, Arnold has $$525$ saved in September.

If the guitar is on sale for a $30%$ discount off the original price of $$650$, then the sale price of the guitar is $100%-30%=70%$ of $$650$, which is equal to $(0.7)\cdot $650 = $455$.

Adding the $5%$ sales tax to the sale price of the guitar, the total cost of the guitar becomes $(1+0.05)\cdot $455 = $477.75$.

Arnold has $$525$ saved in September, and the total cost of the guitar is $$477.75$, which means that Arnold has enough money to buy the guitar in September.

Therefore, Arnold has enough money to buy the guitar in September, and he would have $$525-$477.75=$47.25$ left over after buying the guitar.

Answer 2

Yes, Arnold has enough money to buy the guitar in September. In March, Arnold had $\$300$. In September, $75\%$ of this amount would be $\$225$, and with the $30\%$ discount, the guitar would cost $\$455$. Then, the sales tax would be $5\%$ of the sale price, which would be $\$22.75$, bringing the total cost to $\$477.75$. Therefore, Arnold has $\$477.75$ in September, which is enough to buy the guitar.