Creating and manipulating expressions and formulae

Can you find the value of t in these equations?

If $a \times b=2$, $b \times c=24$, $c \times a=3$ and $a$, $b$ and $c$ are positive, what is the value of $a+b+c$?

Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?

What does the sum of these three numbers tell us about their product?

If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.

Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the road (at 4 miles per hour)...

Relate these algebraic expressions to geometrical diagrams.

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

Can you find a rule which connects consecutive triangular numbers?

Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?