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Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

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Which Is Cheaper?

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Which Is Bigger?


Mike, James, Toby, Molly and Harry from Highfields School, Owen, Estee and Emma from Montessori School, Connor from Gladesmore School, and Karnan from Stag Lane Junior all came up with a similar explanation for the first part of the problem.

Jasmine from Highfields explained:

I plotted both equations on a graph. From this I found out that they both intercept when x=7 Therefore from the graph I have found that:
When n=7,both equations are the same value
When n< 7, n+10 is the biggest
When n> 7, 2n+3 is the biggest
Charlie and Alison got different answers because one person chose a value below 7 and one person chose a value above 7. This method works with every set of equations where you have to find the biggest.

Zak explained how a graph helped:
From looking at this graph we can see that the line with the equation 2n+3 has a larger gradient and so overtakes the line with the equation n+10 even though it starts off lower, so because 2n+3 has a larger gradient it will be larger after n=7.   
We also received some solutions as documents which you can download below:

Rajeev from Haberdashers' Aske's Boys' School
Niharika from Leicester High for Girls
Shivin from the British School, Manila
Siddhartha from Beijing City International School
Amar from Wilson's School
Well done to you all!