SOLUTION: I am having trouble learning how to write the algebraic expressions for word problems. I can solve the problems if I have the expression, but can't figure out how to get the probl

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Question 342918: I am having trouble learning how to write the algebraic expressions for word problems. I can solve the problems if I have the expression, but can't figure out how to get the problem? Example : The sum of 2 brothers' ages is 38. One brother is 10 years older than the other. How old is each brother? Example 2: Matthew loaned three friends a total of $27. All he can remember is that he loaned the second friend $5 more than the first and the third friend twice as much as the second. How much did he loan each of the 3 friends? Any help would be greatly appreciated. thanks!
Found 2 solutions by Alan3354, kcanil08:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
The sum of 2 brothers' ages is 38. One brother is 10 years older than the other. How old is each brother?
Assign symbols, just for convenience.
y = younger brother
e = elder brother (o could be misinterpreted to be a zero)
Then write down what it says.
y + e = 38 (the sum is 38)
e = y + 10 (10 yrs older)
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Example 2: Matthew loaned three friends a total of $27. All he can remember is that he loaned the second friend $5 more than the first and the third friend twice as much as the second. How much did he loan each of the 3 friends?
f1 = amount to 1st
f2 = to 2nd
f3 = to 3rd
f1 + f2 + f3 = 27
f2 = f1 + 5
etc

Answer by kcanil08(11) (Show Source):
You can put this solution on YOUR website!
Problem1:
let the ages be x and y.
as the sum of thrie age is 38.
x+y=38....eqn 1
and one is 10 years older than other means
x+10=y
now just simple math
substututing value of y in eqn 1
x+x+10=38
so x=14
&y=x+10=24
.
.
Problem2:
let us suppose he gave x $ to first fren.
it is said he gave 5$ more to 2nd than to first. so he gave (x+5) $ to 2nd.
also he gave double of 2nd to 3rd. so he gave (x+5)*2 $ to 3rd.
as matthew in total gave 27 $,
x+(x+5)+(x+5)*2 = 27
x+x+5+2x+10=27
4x=27-15
4x=12
so x=3
.
.
therefore
loan to 1st friend = x = 3$
loan to 2nd friend = x+5 = 8$
loan to 3rd friend = (x+5)*2 = 16$

(hope this help. please post one question in one post....i like solve problems but when there are two problem mixed i just leave, in most of the cases..if you have more problems email me. my email is akc2@uno.edu)