SOLUTION: could you help to solve this problem and show in a equation . One number is 8 more than another. If the sum of the smaller number and twice the larger number is 46, find the t

Question 88039: could you help to solve this problem and show in a equation
. One number is 8 more than another. If the sum of the smaller
number and twice the larger number is 46, find the two numbers.

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
When you read the problem, it becomes apparent that you need to find a small number and a
larger number. For ease of understanding and identification, call the Small number S and the
Larger number L.
.
The first sentence tells you that one number is 8 more than another. If it is 8 more, then
this means that it is L. So you should get the idea that if you take 8 away from L then you
should have S. You can write this as:
.
L - 8 = S
.
or by adding 8 to both sides, it may be clearer to you as S + 8 = L. Either one is OK to use.
.
The second sentence tells you that the sum of the Small number (S) and twice the Larger number
(2*L) equals 46. Writing this in equation form gives you:
.
S + 2L = 46 <- call this the second equation
.
Then, from the first equations you can either use the fact that S = L - 8 or that L = S + 8
and substitute into the second equation. For ease, let's use S = L - 8 and so we can replace
S in the second equation with L - 8 to get:
.
L - 8 + 2L = 46
.
Next you can get rid of the -8 on the left side by adding 8 to both sides. When you do
this addition you get:
.
L + 2L = 54
.
Add the terms on the left side and the equation reduces to:
.
3L = 54
.
Finally divide both sides by 3 to reduce the equation and solve for L:
.
L = 54/3 = 18
.
Now you know that L = 18 you can solve for S. You know that L is 8 larger than the smaller
number S. So you can subtract 8 from L and you have S. Therefore, L - 8 = 18 - 8 = 10. Therefore,
S is 10.
.
So the two numbers are 10 and 18.
.
Obviously the larger number is 8 more than the smaller number. Then check further by
adding the smaller number to twice the larger. If you do you get 10 + 2*18 and this becomes
10 + 36 and this equals 46, just as the problem says it should.
.
Hope this helps you to understand the problem and how to solve it.
.
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