SatsMuncher 6: The Algebra Challenge Any Problems?  Remember, you can Ask an Expert

Can You Solve These Ten Puzzlers?  Sometimes the answer is  a number like 2,           ... Sometimes an expression (like c + 2)              ... And sometimes an equation (like a = c + 2).  If you need to, you can get a hint on getting started from the examples below each question.  Good luck! ...   Q1.  If a - 20 = 40, what is the value of a? Example: When I spend £20 of my birthday money, I still have £40 left.  How much did I start with?   Q2.  b + c = 30.  If b = 14, what value is c? Example: I spend 30p altogether on two packets of mints.  If the FreshaBreath mints cost 14p, how much are the the Snuff-2-Blow-Your-Socks-Off Mints?   Q3.  I think of a number and call it u.  I add 8 to that number.  Write an expression to show the result. Clue: Try replacing u with a number such as 2 and write down an expression that works.  Then replace u in the expression ...

Q4.  Simplify the expression 4u + 7u + 10. Example: I've sorted my spending money for the week onto money bags.  I put the same number of pound coins (u) into each bag. (So 3 bags for example would mean 3u pounds.) I spent 4 bags on Monday, 7 bags on Tuesday and a £10 note on Wednesday.  Write an expression to show how much I spent. Q5.  What is half of 8u? Example: On Thursday I take 8 money bags, but I only spend half of the money. Write an expression to show how much I spent.   Q6.  2u + 5 = 11.  What is the value of u? Example: I spent 2 bags and £5 on Friday.  Altogether, I spent £11. How much is in each money bag?    Q7.  4v = 8.  What is the value of 5v? Example: I buy four DVD vouchers for £8.  They are each worth the same (call it £v). How much is each voucher worth?      Q8.  2v + 4w = 16.  Write an expression that is equal to 32. Example: On my last birthday,  I get two identical DVD vouchers and four identical book vouchers.  I spend exactly £16. On this birthday, I get vouchers worth twice as much.  How many vouchers might there  be?

Q9.  I buy a plank of wood 5 metres long.    I divide it into two pieces. If one piece is n metres, can you write an expression for the length of the other piece? Hint: Try replacing n with a number such as 6 and write down an equation that works.  Then replace with n in the equation ...   Q10.  Write an equation that shows that y is four more than twice x. Hint: Try replacing y and x with two numbers and write down an equation that works.  Then replace with x and y in the equation ...