one number is five more than another and their sum is three less than three times the smaller.find the numbers

Answer 1

y = x + 5
x + y = 3x - 3

x + (x + 5) = 3x - 3
2x + 5 = 3x - 3
x = 8
y = 13

Answer 2

"one number is five more than another..."

Let x be the smaller number. This makes sense because, reading ahead, a second explicit reference occurs to the smaller number. If x is the smaller number, then 5 more than that, or x + 5, is the larger number.

"...their sum is..."

We are now talking about adding the two numbers and getting a result. At this point, our equation - the equals sign is math notation for "is" in this context - now looks like this:

(x + 5) + x = ...

"...three less than..."

In other words, we are subtracting three from something on the right. Our equation now looks like:

(x + 5) + x = ? - 3

"...three times the smaller [number]." We already assigned x to the smaller number, so three times this number is 3x. Our equation is now complete:

(x + 5) + x = 3x - 3

"Find the numbers." In other words, find and report both numbers. It is not enough just to solve the equation for the x, the smaller number, but you must then use that result to find x + 5, the larger number.

The equation for x simplifies to

2x + 5 = 3x - 3

Subtracting 2x from both sides gives

5 = x - 3

Adding 3 to both sides gives

8 = x, which is the smaller number. Substituting 8 for x into the expression x + 5 gives 13 for our larger number.

Answer 3

Let x= smallest number
Let y= bigger number

One number is five more than another. More indicates addition... So y= x + 5, because it's 5 bigger than the smaller number, right?

If I add the two numbers up, x + y, the result is 3 less than three times the smaller (3x). Therefore, x + y = (3x) - 3. Since you already solved for y (=x+5), you want to plug in x+5 in all the y's you see in the equation I created above.

X + X + 5 = 3x - 3. Rearrange and solve for X. That gives you the value of the smaller number, then you add 5 and get the value of the bigger number.

Answer 4

Let x = (one number)
y = (another)

translation tip
(one number) is five more than (another )
x is 5 more than y
x = y + 5

their sum is three less than three times the smaller
(their sum) is 3 less than (3 times the smaller)
(x + y) is 3 less than (3 times y)
(x + y) is 3 less than (3y)
x + y = 3y - 3
y+5 + y = 3y -3
y = 8
x = 13

Answer 5

x = y + 5
x + y = 3y - 3

y + 5 + y = 3y - 3
2y + 5 = 3y - 3
5 = y - 3
y = 8
x = 8 + 5 = 13

Answer 6

y = x + 5
x + y = 3x - 3

x + x + 5 = 3x - 3
2x + 5 = 3x -3
x = 8
y = 13

Answer 7

n=5+y
y+n=3y-3

2y+5=y-3
y=8
n=13

Answer 8

so in other words...
x=y+5
and
x+y=3y-3

I'll bet you can do it now.

Answer 9

8,13