Algebra Studio

Final round

Ten problems from the whole studio. Nothing tells you which idea to use. 0 of 10 solved

school

A mother is four times as old as her son. In 20 years she will be twice as old as him. How old is the son now?

school

One candle is 30 cm tall and burns 2 cm an hour. Another is 24 cm tall and burns 1.5 cm an hour. After how many hours are they the same height?

school

A test has 20 questions. A right answer scores 5 and a wrong one loses 2, and every question is answered. Sam scores 58. How many did he get right?

school

Factor $2x^2 + 7x + 3$ .

school

How many integers x satisfy $|2x - 7| < 5$ ?

school

A positive number plus its square is 56. What is the number?

high school

A shop's daily profit, when it sets its price at x, is

P = -2x^2 + 40x - 50.

What is the largest profit it can make?

high school

Solve $2^{x+3} - 2^x = 56$ .

high school

A sequence starts 3, 6, 12, 24, … and each term doubles. Which term is the first to be larger than 10,000?

high school

What is the real part of $(1 + 2i)^3$ ?