SOLUTION: Am having troubles figuring out the 2 expressions to use in solving this problem: The sum of 2 number is 311. One quarter of the larger is four more than the smaller number. What

Question 66794: Am having troubles figuring out the 2 expressions to use in solving this problem: The sum of 2 number is 311. One quarter of the larger is four more than the smaller number. What are the two numbers.
I know the first expression is x + y = 311
I can't figure out how to make the second expression to solve for both.(does that make sense?)
Thank you for whatever help you can give. I'm most frustrated with this at the moment and I'm sure it's something simple I'm missing.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=smaller number
Any y=larger number
We are told that the sum of these two numbers is 311. So we have our first equation just as you said: YOU GOT THE FIRST EQUATION!!!!!! THAT'S A START.
(1) x+y=311
Now we are also told that one quarter of the larger number (1/4)y is 4 more than the smaller number (4+x). So we have our 2nd equation
(2) (1/4)y=x+4 subtract x from both sides
(2a) -x+(1/4)y=4
add (1) and (2a) and we get:
y+(1/4)y=315 multiply every term by 4
4y+y=1260
5y=1260
y=252------------ Larger number
substitute y=252 in (1)
x+252=311 subtract 252 from both sides
x=311-252=59-----------Smaller number
ck
sum=311;
252+59=311
311=311
1/4 of larger number is 4 more than the smaller number;
(1/4)(252)=59+4
63=63
Hope this helps----ptaylor

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