SOLUTION: One number is 5 more than another. 5 times the smaller equals 4 times the larger. Find the numbers. Thank you!! I struggle with these :(

Question 249094: One number is 5 more than another. 5 times the smaller equals 4 times the larger. Find the numbers.

Thank you!! I struggle with these :(
Found 3 solutions by stanbon, Earlsdon, jim_thompson5910:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
One number is 5 more than another. 5 times the smaller equals 4 times the larger. Find the numbers.
----------------------
Equation:
x = y+5
Note: y is the smaller number.
------------
5y = 4x
-----------------
Substitute for "x" and solve for "y":
5y = 4*(y+5)
5y = 4y+20
y = 20 (smaller number)
-----
x = y+5 = 25 (larger number)
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Cheers,
Stan H.
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Let A be the smaller number and B the larger.
1) B = A+5 "One number (B) is 5 more than another (A)"
2) 5*A = 4*B "5 times the smaller (A) equals 4 times the larger (B)."
Substitute 1) into 2)
3) 5*A) = 4*(A+5) Simplify.
3a) 5A = 4A+20 Subtract 4A from both sides.
3b) A = 20 and...
1a) B = A+5
1b) B = 20+5
1c) B = 25
The numbers are: 20 and 25
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Let x=the first number, y=second number

The phrase "One number is 5 more than another" can be broken up as:

So "One number is 5 more than another" translates to

Note: this implies that ie 'y' is the smaller number.

Similarly, "5 times the smaller equals 4 times the larger" can be represented as

So "5 times the smaller equals 4 times the larger" translates to

So we have the two equations

Start with the first equation.

Subtract 5 from both sides.

Rearrange the equation.

Move onto the second equation.

Plug in (this works since we're dealing with the same 'y').

Distribute.

Add to both sides.

Subtract from both sides.

Combine like terms on the left side.

Go back to the first isolated equation.

Plug in

Subtract.

So the solutions are and giving us the ordered pair (25,20)

So the smaller number is 20 and the larger is 25.
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