Mates Erica Trial Exam 1

81^2 * 27^3 = 3^x. Write x

Simplify fully

Simplify fully

Problem Solving Questions: 1a) Erica used to love reading. The year she was 11, she read 70% more books than she read this year, at 13. The year she was 12, she read 35% fewer books than she read this year. In total, she has read 335 books over these three years.How many books did Erica read this year?

1b)Next year, Erica wants to be the person who reads the most books in her class, but Matias is also reading a lot.

• Suppose this year, Erica read 50% of the books she will read next year.

• Matias, when he was 12, read 40% of the books he read at 13, which was 50 books.

• Matias originally thought he would read more 120% of what he read at 13. Will Erica read more than Matias next year?

Erica and Matias are also competing to see who reads the most fiction books.

• This year, 80% of Matias' books were fiction, while only 60% of Erica's books were fiction.

• Next year, Matias will have read 80% of the fiction books he will read next year.

• Erica will have read 70% of the fiction books she will read next year. Who will read more fiction books next year?

Erica has always dreamed of buying a Mini Cooper, which costs $25,000. She starts saving by depositing $5,000 into a high-yield savings account that earns 6% annual interest, compounded annually. She plans to let the money grow for 5 years before buying the car.

However, after 3 years, her old car breaks down, and she needs to withdraw $2,000 for urgent repairs. She leaves the remaining money in the account for the final 2 years. a)How much money does Erica have after 3 years (before withdrawing)?

b)How much is left after she withdraws $2,000?

c) How much does Erica have at the end of 5 years (after interest on the remaining balance)?

d) How much more does Erica need for the Mini Cooper?