# Resources tagged with: Other equations

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### There are 16 results

Broad Topics > Algebraic expressions, equations and formulae > Other equations ### Old Nuts

##### Age 16 to 18Challenge Level

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start? ### Root to Poly

##### Age 14 to 16Challenge Level

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$. ### Polynomial Relations

##### Age 16 to 18Challenge Level

Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one. ### Real(ly) Numbers

##### Age 16 to 18Challenge Level

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have? ### Rudolff's Problem

##### Age 14 to 16Challenge Level

A group of 20 people pay a total of Â£20 to see an exhibition. The admission price is Â£3 for men, Â£2 for women and 50p for children. How many men, women and children are there in the group? ### Our Ages

##### Age 14 to 16Challenge Level

I am exactly n times my daughter's age. In m years I shall be ... How old am I? ### Coffee

##### Age 14 to 16Challenge Level

To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used? ### Building Tetrahedra

##### Age 14 to 16Challenge Level

Can you make a tetrahedron whose faces all have the same perimeter? ### Deep Roots

##### Age 14 to 16Challenge Level

Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$ ### Are You Kidding

##### Age 14 to 16Challenge Level

If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle? ### Hand Swap

##### Age 14 to 16Challenge Level

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . . ### Around and Back

##### Age 14 to 16Challenge Level

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . . ### One and Three

##### Age 14 to 16Challenge Level

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . . ### Hike and Hitch

##### Age 14 to 16Challenge Level

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. . . . ### Three Four Five

##### Age 14 to 16Challenge Level

Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles. ### Golden Ratio

##### Age 16 to 18Challenge Level

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.