Please help my daughter on these challenging questions
My daughter age 11 was given these problems, which she was unable to do. We would be grateful to have answers by tomorrow (Smirk)
Could someone be please kind enough to explain her the answers, in the simplest way possible (she's only 11!).
Here are the problems:
1) Inflation is running at 5% per year. This means that, for example, if a certain amount of any commodity costs £1 this year, the same amount will cost £1.05 in a year's time.
A merchant decides to sell a quantity of gold, then invest the money at an interest rate of a% per year, then after 1 year spends this money (with its interest) on buying gold again. He finds that he can buy 10% more gold than he had originally sold! What was the value of a?
2) A train travels for 10 miles at 30mph, then the next 10 miles at 60mph, and the average speed for the whole journey is 42 6/17mph (this is made of a whole number 42 and a fraction 6/17). What fraction of the distance of the whole journey is the first (30mph) part?
3) In this question x * y means (x+2y)/3 if x < y, and (2x + y)/3 if x is larger or equal to y.
In terms of p and q, find the possible values of (p * q) *p, explaining carefully how you choose which calculations to make.
4) Draw an X and Y plan, with the coordinates of O being your origin (0,0). Plot A with coordinates (2,0), B (3,0) and C (2,1).
Now in this question journeys are made of steps of whole-numbers length in any combination of directions left, right, up or down. Also one may retrace steps. So, for example, it is possible to travel from O to the point (2,1) by journey OAC which has length 3, it is possible to get to (2,1) by a different journey, OBAC which has length 5.
a) Starting from O, how many possible destinations (including O) are there with journeys of length
b) How many different journeys of length 3 are there starting at O and finishing at (1,0)?
c) You are given that the sum 1+2+3+....+100 = 5050
How many journeys of length 102 are there from O to coordinate (100,0)?