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The age of one brother combined with twice the age of a second brother is 50. The difference between twice the age of the first brother and the age of the second brother is 10 years. SOLUTION:OK, first a definition: --> Let x = age of first brother --> Ley y = age of second brother. In questions like this, we generally have 2 unknowns. If that is true, then we need enough information to generate 2 equations from which to solve both unknowns. Again, we usually have 2 sentences, each one will produce one of the required equations. Looking at the sentence:"The age of one brother combined with twice the age of a second brother is 50" we need to convert this to algebra, so "The age of one brother" "combined with" "twice the age of a second brother" "is" "50"________x__________ ______+_____ ___________2y___________ __=__ _50_ if you EVER get stuck converting something like "twice the age of a second brother", then just pick examples, eg IF he was 10, then twice his age would be (10+10 OR 2*10) --> 20so, IF he was y, then twice his age would be (y+y OR 2*y) --> 2y --> x+2y = 50 Looking at the next sentence:"The difference between twice the age of the first brother and the age of the second brother is 10 years", so "The difference between twice the age of the first brother and the age of the second brother is 10"___subtract them____ ____________2x______________ _____________y_______________ _=_ _10_ again, if confused, pick 2 easy numbers to test your translation: eg the difference betwee 10 and 6 is? well the answer is 4, gotten from 10-6 --> 2x-y = 10 So we have 2 equations now, which need solving: this is another topic ;-) ===========================================================================================
The ages of a father and son now add up to 40. In 6 years time, the difference in their ages will be 24 years. What are their ages now? SOLUTION:First, the defintion, again: --> Let x = age of father NOW. --> Let y = age of son NOW. "The ages of a father and son now add up to 40."--> x + y = 40 "In 6 years time" --> what are their ages then if they are x and y now? Well, if someone is 30 now, how old will they be in 6 years? Answer is 30+6. So, if someone is x now, in 6 years time, they will be x+6. So, "In 6 years time, the difference in their ages will be 24 years"--> (x+6) - (y+6) = 24 It is this way round rather than (y+6) - (x+6) = 24, because the father is older ie has a larger age. The second equation becomes x - y = 24 and we then solve these as normal.
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