# Maths Problem of the Week

20/10/2020
title

A species of plant can have one to five flowers. The probability of each number of flowers is given by:

 Number of Flowers Probability 1 2 3 4 5 0.12 0.24 0.23 0.2

Peter plants 96. How many of Peter's plants will have three flowers?

13/10/2020
What is the smallest number of beans?

A bag contains some red, some yellow and some blue beans. The probability of picking a red bean at random is 0.2. It is known that the ratio of yellow to blue beans is 5:7

06/10/2020
Time to Fill up the Pool

The pool can be filled by a big pump in 5 hours and by a small pump on 20 hours.
How long will both pumps take to fill the pool?

08/09/2020
Find the next three terms in this sequence

14, 24, 36, 50, 66, ..., ..., ...,

01/09/2020
Find ∠ABC

A C and D are point on a circle centred O;
AB and CB are tangents to the circle;
AD and CD are chords in the circle;

25/07/2020
Solve Simultaneously

$\sqrt{x}+y=11$

$x+\sqrt{y}=7$

Solution:
The equations imply that x, y > 0
Both equations have integers of the RHS
implying x, y, sqrt x, sqrt y are elements of the integers
moreover x, t are perfect squares
so 0 < x < 7 and 0 < y < 11
So $x\in \left\{1,4\right\}$ and $y\in \left\{1,4,9\right\}$
Therefore x = 4 and y = 9
Are there any other solutions?

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