SOLUTION: Can I please get help on this word problem? The sum of two numbers is 46. Four times one number is 4 more than twice the other number. Find the numbers. So far I have tried many ti

Question 252089: Can I please get help on this word problem? The sum of two numbers is 46. Four times one number is 4 more than twice the other number. Find the numbers. So far I have tried many times but always end up with an impossible answer. One thing I have tried is, 4x + 2x + 4 = 6(42). But I always end up getting 41 and 1/3. Can you please teach me how to do this problem?
Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sum of two numbers is 46. Four times one number is 4 more than twice the other number. Find the numbers
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Equations:
x + y = 46
4x = 2y+4
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Rearrange:
x = 46-y
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Substitute for "x" and solve for "y":
4(46-y) = 2y + 4
184 - 4y = 2y + 4
6y = 180
y = 30
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Since x = 46-y, x = 46-30 = 16
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Solution: x = 16 ; y = 30
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Cheers,
Stan H.
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Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
First we have two unknowns and need two equations.
The first thing we learn is the two numbers add up to 46
n+m=46
Now the next part is a bit hard to understand so lets break it down.
(four times one number)4n
It doesn't matter at this point which one- n or m will do.
so I choose n
then it says that 4n is (means =} 4 more (4+ )than twice the other number 2m
4n=4+2m
so now we have our two equations in two unknowns
n+m=46
4n=4+2m
solve the first one for either m or n it doesn't matter
n=46-m
or
m=46-n
just choose one and stick with it all the way
4n=4+2m
every time we see n in the above equation we will put 46-m
4(46-m)=4+2m
now we have one equation with one unknown
so now we just have bring everything together and combine and get the all the m's on one side and all the numbers on the pother
first let's multiply out
4*46-4m=4+2m
add 4 m to both sides
4*46=4+6m
4*45+4*1=4*1+6m
subtract 4*1 from both sides
4*45=6m
(2*2)*(3*15)
2*3*2*15=6m
6*30=6m
divide by 6
30=m
46-m=n
46-30=n
16=n
so far so good
now we go back to the second equation and check our work
4n=4+2m
4*16=4+2(30)
64=64
ok

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