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 :(

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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) About Me  (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.
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Equation:
x = y+5
Note: y is the smaller number.
------------
5y = 4x
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Substitute for "x" and solve for "y":
5y = 4*(y+5)
5y = 4y+20
y = 20 (smaller number)
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x = y+5 = 25 (larger number)
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Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (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) About Me  (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 x=5%2By

Note: this implies that x%3Ey 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 5y=4x


So we have the two equations system%28x=5%2By%2C5y=4x%29


x=5%2By Start with the first equation.


x-5=y Subtract 5 from both sides.


y=x-5 Rearrange the equation.


5y=4x Move onto the second equation.


5%28x-5%29=4x Plug in y=x-5 (this works since we're dealing with the same 'y').


5x-25=4x Distribute.


5x=4x%2B25 Add 25 to both sides.


5x-4x=25 Subtract 4x from both sides.


x=25 Combine like terms on the left side.


y=x-5 Go back to the first isolated equation.


y=25-5 Plug in x=25


y=20 Subtract.


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


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