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Written Equations: Algebra



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Wed May 04, 2011 1:38 am
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Lavvie says...



So we're doing algebra but with written equations. These are the two questions I can't get past. By the way, I have translated it from French so if there is any confusion, it's my translating skills xD


1) Julie and Louise's aged added equal 28. In 8 years, Louise will be triple Julie's age. What is the age of each person?

2) Split 39 into two parts so that 3 times the biggest number and 5 times the smallest equal 151.
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Wed May 04, 2011 1:47 am
Lethero says...



Number One is 25 and 3.
25+3=28
(25+8)/3=3+8

Number two is 22 and 17.
22+17=39
3(22)+5(17) = 66+85=151
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Thu Jun 16, 2011 12:12 pm
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Squall says...



Although Varg has the right answer, I dislike the lack of an algebraic approach in his method. This is how I would do it.

In questions like this, be sure to donate what the question as x (the unknown that we are trying to work out). In the first question, I'm going to donate x for one of the two girls

Let x be one of the girl's age.

Because the question says that the age of Julie and Louise add up to 28, the other girl's age must therefore be:

28 - x.

It then says that in 8 years, Louise will be 3 times older than Julie. With that, we can set up our simple equation:

3 ( 28 - x + 8 ) = x + 8

108 - 3 x = x + 8

100 = 4x

x = 25.

Therefore, Louise's current age is 25.

But we have not finished yet, we still need to get Julie's age. Julie will just be 28 - 25 = 3 since the sum of those two girls' ages adds up to 28.

So therefore, Louise's current age is 25, and Julie's current age is 3.
___________________________________________

The second question requires a similar approach to the first one. Here, I'll let x be the smaller number since it'll be easier to work with. Therefore, the bigger number is 39 - x . Now to solve it with the information given:

3 ( 39 - x ) + 5x = 151

117 - 3x + 5x = 151

117 + 2x = 151

2x = 34

x = 17

Therefore, the smallest number is 17, and the bigger number is (39 - 17) which is 22.
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