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Chrissy68

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Trying to help my daughter work out this problem on an algebra exercise paper and struggling greatly, any help would be appreciated, T.I.A. ...A worker's salary is €950 per month and each year it increases by €50 (each month), calculate how much money he will earn in the next 10 years.
 
That's relatively straightforward, though perhaps a little tedious, to do by simple arithmetic. Initially the pay is €950 per month so the first year he will earn a total of 12(950)= 11400. The next year his salary goes up to €950+ 50= €1000 so the second year he earns 12(1000)= €12000. The next year his salary goes up to €1000+ 50= €1050 per month so the third year he earns 12(1050)= €12600. Continue doing that until you have calculated how much he earns the tenth year then add them all.

If you want a little more "sophisticated"- and a little faster- method, think of those as "12(950+ (950+ 50)+ (950+ 2(50))+ (950+ 3(50))+ …+ (950+ 9(50))+ (950+ 9(50)))". There are 10 "copies" of 950 added to 50+ 2(50)+ ...9(50)= 50*(1+ 2+ 3+...+ 9) then multiplied by 12. Adding 950 10 times gives 10(950)= 9500. To calculate 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9 (if direct addition is too tedious!) think of it as (1+ 9)+(2+ 8)+ (3+ 7)+ (4+ 6)+ 9= 10+ 10+ 10+ 10+ 9= 49. Multiply 49+ 9500= 9549 by 12.
 
Hi, yes I get that and I worked it out like that but I think an algebra method is needed, to be worked out as an equation and that’s what I don’t get... my answer is different?
 

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Your work looks perfect to me.

HallsofIvy made two careless mistakes. In summing 1+2+3+...+9 he suggested to instead sum (1+9)+(2+8)+ (3+7) + (4+6) + 9. That last 9 was wrong as you can see that the 9 was already added. There is no 5 being added so that 9 should be a 5. The second error made was that the 49 (which should have been 45) was NOT multiplied by 50.
 
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12[ (950) + (950 + 1*50) + (950 + 2*50) + (950 + 3*50) + ... + (950 + 9*50)]

=12[ 950*10 + 50(1+2+3 +...+9)] = 12[950*10 + 50(45)]= 12[9500 + 2250] = 12[11750] = 141,000.

Same answer as you got!!! Just be careful!
 
One of the reason it states in the guidelines that you show us your work is because we want to see how you want to do the problem. Prof Halls spent a great deal of time answering your question but he was way off as far as doing it the way that you wanted it done.

So please in the future show us your work, tell us which method you would like to use, what was recently taught in the class, etc as this will help us understand which method you want to use.
 
Sorry, I think you have misunderstood me.
I worked the answer out the same way as Prof Halls aswell. I was asking for the algebra equation way of doing it and an explanation. The workings out , I attached, was the method and answer the school wants it done. basically I don’t understand that method! Sorry been 35 years since I did algebra! I did state that an algebra method was required! Thank you.
 
so this is the lame way I worked it out, but needs to be in an algebra equation.
hope you understand me.
 

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Chrissy68 said:
Trying to help my daughter work out this problem on an algebra exercise paper and struggling greatly, any help would be appreciated, T.I.A. ...A worker's salary is €950 per month and each year it increases by €50 (each month), calculate how much money he will earn in the next 10 years.
Click to expand...
Does your daughter know "sum of n terms in arithmetic progression"?
 
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