There is much confusion and scratching of heads and gnashing of teeth on topics where you have English sentences that have to be converted into maths.
The secret is twofold. First, practice and secondly more practice. There is not a lot of much else really. That said, here are some notes on trying to help you decipher the English.
Method of Working that I do every time:
I read the question and eventually it tells me what they want me to find, beit "ages now" or whatever. These will be the basis of my definitions.
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.
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) --> 20
so, 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?
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.
EXAMPLES FROM THE WEBSITE
: I REALLY NEED HELP WITH THESE PROBLEMS, ITS DUE TOMORROW AND I CANT SEEM TO GET THE ANSWERS TO THESE PROBELMS..IT IS ABOUT VERBAL PROBLEMS..THANKS!
THREE LESS THAN FIVE TIMES A CERTAIN NUMBER IS EQUAL TO 67 MORE THAN ONE-THIRD OF THE NUMBER. FIND THE NUMBER.
THANKS AGAIN!See answer to question 26744
: Hi, my name is Marissa.
I was wondering if you could show me how to solve this problem?
Okay it says, Use P=4s to find the perimeter of each square
#1. s= 12ft.
Please help I really don't understand, Thanks MarissaSee answer to question 26714
|Answer #14531 by longjonsilver(2297) |
You can put this solution on YOUR website!
perimeter means add up all the lengths of the sides of the shape. Now a square is a 4-sided shape where all four sides are the same length...that is what a square is.
So, instead of adding up 4 identical numbers, like for example 3+3+3+3, we could re-write this as 4x3...multiplication is a quick way of adding like things.
So, that is what the question has given you. It has said the side is of length s and being a square, all 4 sides are of length s so the perimeter P is s+s+s+s OR P is 4s (meaning 4 times s).
So, using this formula, and given that s=12, find the perimeter.
: Two angles are supplementary. One angle is 28 degrees less than 3 times the other angle. Find the angles.See answer to question 26721
: Two angles are complementary. One angle is 15 degrees more than 2 times the other. Find the angles.See answer to question 26720
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