SOLUTION: I am 60 and trying to help my kids with this problem. It's been a while since college. Please help with the formula. 3 numbers added equal 500. The second number is 4 times the

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Question 995553: I am 60 and trying to help my kids with this problem. It's been a while since college. Please help with the formula.
3 numbers added equal 500. The second number is 4 times the first and the third is 5 times the second. find each number.
Thanks
Tom
Found 3 solutions by stanbon, Theo, ankor@dixie-net.com:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
3 numbers added equal 500. The second number is 4 times the first and the third is 5 times the second. find each number.
Thanks
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1st number: x
2nd number: 4x
3rd number: 5(4x) = 20x
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Equation::
x + 4x + 20x = 500
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25x = 500
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Divide both sides by 25 to solve for "x"::
x = 20
----
1st number x = 20
2nd number: 4x = 80
3rd number: 20x = 400
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Thanks for helping. Keep up the good work.
Cheers,
Stan H.
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Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
numbers are a, b, and c
a + b + c = 500
second number is 4 times the first.
b = 4 * a
third number is 5 times the second.
c = 5 * b

in the original equation of a + b + c, replace c with 5 * b to get:

a + b + 5 * b = 500

now replace b with 4 * a to get:

a + (4 * a) + (5 * (4 * a)) = 500

remove parentheses to get:

a + 4 * a + 5 * 4 * a = 500

simplify by performing the indicated operations to get:

a + 4 * a + 20 * a = 500

comeine like terms to get:

25 * a = 500

divide both sides of the equation by 25 to get:

a = 500 / 25 = 20

if a = 20, then b = 4 * a makes b = 4 * 20 = 80, and c = 5 * b makes c = 5 * 80 = 400.

a + b + c = 500 becomes 20 + 80 + 400 which becomes 500 = 500.

this confirms the solution is good.

solution is:

a = 20
b = 80
c = 400

first number is 20.
second number is 4 * first number = 80
third number is 5 * second number = 400

Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
Write an equation for each statement
:
3 numbers added equal 500.
a + b + c = 500
The second number is 4 times the first
b = 4a
or
a = .25b
and the third is 5 times the second.
c = 5b
:
find each number.
Substitute for a and c in the first equation
.25b + b + 5b = 500
6.25b = 500
b = 500/6.25
b = 80
:
You can find a and c now. See that they add up to 500