SOLUTION: Please help me to solve this problem - The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers.

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Question 1124727: Please help me to solve this problem - The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers.
Found 3 solutions by MathLover1, josmiceli, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let's two numbers be x and y
if the sum of two numbers is 2490, we have
x%2By=2490....eq.1
if 6.5%=0.065 of one number is equal to 8.5%=0.085} of the other, we have
0.065x=0.085y
x=0.085y%2F0.065
x=1.307692307692308y............eq.2

substitute in eq.1
1.307692307692308y%2By=2490....eq.1
2.307692307692308y=2490
y=2490%2F2.307692307692308

y=1078.999999...round it
y=1079
x=1.307692307692308%2A1079............eq.2
x=1411.000000000000332...round it
x=1411
check:
x%2By=2490
1411%2B1079=2490
2490=2490->True

0.065x=0.085y
0.065%2A1411=0.085%2A1079
91.715=91.715->True





Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be a and b
(1) +a+%2B+b+=+2490+
(2) +.065a+=+.085b+
—————————————
(2) +65a+=+85b+
(2) +b+=+%2813%2F17%29%2Aa+
Plug this into (1)
(1) +a+%2B+%2813%2F17%29%2Aa+=+2490+
(1) +17a+%2B+13a+=+42330+
(1) +30a+=+42330+
(1) +a+=+1411+
And
(1) +1411+%2B+b+=+2490+
(1) +b+=+1079+
—————————————-
Check:
(2) +.065%2A1411+=+.085%2A1079+
(2) +91.715+=+91.715+
OK

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me to solve this problem - The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers. 
Let smaller number be S

Then larger number = 2,490 - S

We then get: .065(2,490 - S) = .085S

161.85 - .065S = .085S

161.85 = .085S + .065S

161.85 = .15S

S, or smaller number = highlight_green%28matrix%281%2C3%2C+161.85%2F.15%2C+%22=%22%2C+%221%2C079%22%29%29

Larger number: