The Long family spent $38.62 for school supplies and $215.78 for new school clothes. They paid $6\frac{5}{6}\%$ sales tax on their purchases. If the Long family paid $269.07 total, determine if they paid the correct amount.
a. The Long family paid $2.63 too little for their purchases.
b. The Long family paid the correct amount for their purchases.
c. The Long family paid $1.61 too much for their purchases.
d. The Long family paid $2.63 too much for their purchases.
Answer (1)
Calculate the total cost of purchases before tax: 38.62 + 215.78 = 254.40 .
Calculate the sales tax amount: 254.40 × 0.065 = 16.536 .
Calculate the total cost of purchases including tax: 254.40 + 16.536 = 270.936 .
Calculate the difference between the amount paid and the correct amount: 269.07 − 270.936 = − 1.866 . The Long family paid approximately $1.87 too little.
Explanation
Calculate the total cost before tax First, we need to calculate the total cost of the school supplies and school clothes before tax. This is done by adding the cost of the school supplies and the cost of the school clothes: 38.62 + 215.78 = 254.40 So, the total cost before tax is $254.40.
Calculate the sales tax amount Next, we need to calculate the amount of sales tax. The sales tax rate is 6.5% , which can be written as 0.065 . We multiply the total cost before tax by the sales tax rate to find the sales tax amount: 254.40 × 0.065 = 16.536 So, the sales tax amount is $16.536.
Calculate the total cost after tax Now, we need to calculate the total cost of the purchases including tax. We add the total cost before tax and the sales tax amount: 254.40 + 16.536 = 270.936 So, the total cost including tax is $270.936.
Calculate the difference We are given that the Long family paid 269.07. T o d e t er min e i f t h ey p ai d t h ecorrec t am o u n t , w e n ee d t o f in d t h e d i ff ere n ce b e tw ee n t h e am o u n tt h ey p ai d an d t h ecorrec tt o t a l cos t in c l u d in g t a x : 269.07 − 270.936 = − 1.866 R o u n d in g t o t h e n e a res t ce n t , t h e d i ff ere n ce i s -1.87.
Final Answer Since the difference is negative, it means the Long family paid less than the correct amount. The Long family paid $1.87 too little. However, this amount is not present in the options. Let's re-evaluate the problem. The problem states the tax rate is 6 5 − % . This is ambiguous. Let's assume it means 6.5% . If we round the total cost including tax ( 270.936 ) to the nearest cent, we get 270.94 . Then the difference is: 269.07 − 270.94 = − 1.87 This still indicates they paid too little. However, if we look at the options, none of them match this value. Let's re-examine the calculation: Total cost before tax: 38.62 + 215.78 = 254.40 Sales tax: 254.40 × 0.065 = 16.536 Total cost after tax: 254.40 + 16.536 = 270.936 Difference: 269.07 − 270.936 = − 1.866 R o u n d in g t o tw o d ec ima lpl a ces , t h e d i ff ere n ce i s -1.87$. This means the Long family paid $1.87 too little. However, this is not one of the options. There might be a typo in the options. Let's check the closest option. Option a states that the Long family paid $2.63 too little. Option c states that the Long family paid $1.61 too much. Option d states that the Long family paid 2.63 t oo m u c h . S in ce t h ec a l c u l a t e dd i ff ere n ce i s -1.87$, it is closest to paying too little. However, none of the options match the calculated value. Let's assume the total amount paid is 269.07 . Then, the difference is 269.07 − 270.936 = − 1.866 . This means the Long family paid $1.87 too little. Since none of the options match the calculated value, let's check if there is a typo in the total amount paid. If the total amount paid was 270.07 , then the difference would be 270.07 − 270.936 = − 0.866 . This is still not close to any of the options. Let's assume the tax rate is different. If the tax rate was 7% , then the sales tax would be 254.40 × 0.07 = 17.808 . The total cost after tax would be 254.40 + 17.808 = 272.208 . The difference would be 269.07 − 272.208 = − 3.138 . This is still not close to any of the options. Let's assume the total cost of school supplies is 36.62 instead of 38.62 . Then the total cost before tax is 36.62 + 215.78 = 252.4 . The sales tax is 252.4 × 0.065 = 16.406 . The total cost after tax is 252.4 + 16.406 = 268.806 . The difference is 269.07 − 268.806 = 0.264 . This is still not close to any of the options. Given the calculations and the options, it seems there might be an error in the problem statement or the options provided. However, based on the calculations, the closest answer is that the Long family paid too little. The closest value to 1.87 is 2.63 . Therefore, the Long family paid approximately $2.63 too little.
Conclusion The Long family paid approximately $1.87 too little for their purchases. Since none of the options exactly match this value, we choose the closest option, which is that they paid $2.63 too little.
Examples
Understanding sales tax calculations is essential for budgeting and making informed purchasing decisions. For instance, if you're planning to buy a new laptop for $800 and the sales tax rate is 7% , you can calculate the sales tax amount by multiplying the laptop price by the tax rate: $800 × 0.07 = $56 . Therefore, the total cost of the laptop, including tax, would be $800 + $56 = $856 . This calculation helps you understand the final cost and plan your finances accordingly.
