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The first floor of an ancient japanese tower has 150 steps. Each floor above has 5 fewer floors than the previous. So, the second floor has 145 steps, the third 140 etc. How many floors does the tower have if the final floor has 30 steps leading to it.

Note this is an arithmetic series problem, so we use the equation: x_n= a + d(n-1).
Number of steps on the first floor is 'a', i.e. a = 150.
Difference in the number of steps on each ...

Answered by Joel F. • Maths tutor

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The ratio of Adam's age to Bob's age is 1:2. In 12 years time, the ratio of their ages will be 3:5. Calculate their current ages.

Now: In 12 years:A:B A:B1:2x:2x x+12:2x+12 = 3:5
x+12 = 2x+123 55(x+12) = 3(2x+12)5x + 60 = 6x + 36x = 24
A:B Adam = 24, Bob = 48x:2x24:2(24)24:48

Answered by Aaron S. • Maths tutor

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Simplify: 2x + 6y + 2y - x

Step 1) Rearrange the equation as follows: (2x - x) + (6y + 2y) this makes it easier to see which values you can add together.Step 2) Solve the calculation in each bracket: x + 8y. Successfully simplifyin...

Answered by Benjamin L. • Maths tutor

3357 Views

Factorise x^2 + 8x + 12 (2017 non-calculator paper)

This question requires you to work through methodically in stages. We want two numbers, a and b, which fit into brackets of the form: (x + a)(x + b). By doing this, we have simplified the expression throu...

Answered by Ella M. • Maths tutor

3618 Views

Solve the simultaneous equations x + y = 3 and x^2 + y^2 = 5

Find an expression for y
y = 3 - x
sub this into the second equation
x^2 + (3 - x)^2 = 5
then expand the brackets
x^2 + x^2 - 6x + 9 = 5
simplify
2(x^2 - 3x + 2) = 0<...

Answered by Kate W. • Maths tutor

14982 Views