One number plus twice another number gives a sum of 42. The difference of these same two numbers equals –3.

Question

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Answer 1

x + 2y = 42

2[x - y = -3]

3x = 36
x = 12

so, plugging x back in

12 - y = -3
y = 15

Answer 2

Ok, let's write this out symbolically. Call the numbers A and B. (Yeah, we'll get to just one letter in a minute, and I know schools are partial to using x for the unknown, but I begin this way for a reason...)
One number plus twice another gives a sum of 42.
So you have A + 2B = 42
The difference of these numbers is -3
So you have A - B = -3 (wait a minute! Why not B - A = 42? Well, it won't make any difference in the long run...)
Now here's where we get it in terms on one letter. Since A - B = -3, add B to each side and you get A = B - 3.
(Stop and think about two numbers whose difference is 3, say, 5 and 8. 5 - 8 = -3, also 8 - 5 = 3. So far so good.)
Now, take the fact that A = B - 3 and put this where the A lives, in the first equation.
So instead of A + 2B = 42 you have
(B - 3) + 2B = 42
Now you have just one requation with one variable and you can simplifiy and solve. Drop the parenthesis, as you don't really need them, and you get
B - 3 + 2B = 42
Combine like terms (the B's) and you get
3B - 3 = 42 + 3 = 45
Add 3 to each side to get the 3B by itself (you always want to get the letter by itself, that way the answer will be on the other side)
3B = 45
Divide by 3 and you find out that B = 15
Now for A ...
A - B = -3 (from the equation we got earlier)
Substitute B = 15
A - 15 = -3
Add 15 to each side to get the A by itself (again, you want the letter by itself so the answer will be on the other side)
A = -3 + 15 = 12
Check : One number (12) plus twice another (15) = 42
12 + (2 x 15) = 12 + 30 = 42
(Note, if you interchange A and B at this point you'll get different numbers, like someone else did a little ways down,so be careful. Their difference is -3, not 3)
(Note: I use A and B rather than x because it's easier to think of two numbers, two letters, than to try and relate them both from the getgo. Also I use A and B rather than x because this helps overcome math blocks, where the subconscious is tihnking, "x is unknown, I'm not supposed to know it..." If your teacher uses x, that's their business. I've never known a teacher to object to someone using a different letter for the varialbe, as long as they're consistent about it.)

Answer 3

I think that there is no answer to the problem.

There are 2 numbers. For the difference of the numbers to = -3, one of the numbers has to be a negative number where the number itself (without the sign), is 3 greater than the positive number.

When you multiply 2 times a negative number, the sign does not change. Therefore there are 2 ways to set up the equations:

#1 is:
-X+2Y=42
-X + Y= -3

#2 is:
X+2(-Y)=42
X- Y = -3

In #1, in the top equation, 2Y has to be 42> the -X. In the bottom equation, Y has to be 3 less than the X., yet X has to have the same value in the top equation as it does in the bottom one and likewise for the Y. I don't see where that is possible.

In #2, in the top equation, the value of X has to be 21>Y and in the bottom equation, the value of X is 3

Answer 4

Let one number = x and the other number = y

x + y = 42
x - y = -3

2 x = 39
x = 19 1/2

y = 42 - 19 1/2

y = 22 1/2

19 1/2 - 22 1/2 = - 3
19 1/2 + 22 1/2 = 42
Proof

Answer 5

There are two ways to do this, because the question
does not specify which difference should be taken.

The two sets of equations are :

1a) x + 2y = 42
1b) x - y = -3

and

2a) x + 2y = 42
2b) y - x = -3

In the first set, subtracting 1b from 1a gives :
3y = 45, so y = 15. Substituting back gives x = 12.

In the second set, adding 2a to 2b gives :
3y = 39, so y = 13. Substituting back gives x = 16.

So the 2 numbers are either 12 and 15, or 16 and 13.

Answer 6

The direct translation of the word problem is as follows, (for x, y)

x + 2y = 42
x - y = -3

Let's solve this by substitution. x = -3 + y

(-3 + y) + 2y = 42
-3 + 3y = 42
3y = 45
y = 15

Now that we have y = 15, we can get x x = -3 + 15 = 12.

So x = 12, y = 15, is the solution.

Answer 7

x+2y=42 x=42-2y
x-y=-3 x=-3+y

42-2y=-3+y
42=-3+3y
45=3y
y=15
x=-3+15
x=12

Answer 8

x-y=3
x=y+3
x+2y=42 substitute
y+3+2y=42
3y=39
y=13
x=y+3
x=16
check 16+2*13=16+26=42

the numbers are 16 & 13

Answer 9

16 and 13

Edit: Wow, I can't believe I came up with a different answer than other people. You guys used formulas, I just ran it through my head.

13 X 2 = 26
26 +16 = 42

Even better. With a list of right answers greckel posted a wrong answer and gave everyone thumbs down...

Answer 10

the first number is twelve and the second is fifteen