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The sum of two numbers is 2490 . Find the numbers, if 8.5% of the first one is equal to 6.5% of the other .

User Fbiville
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1 Answer

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27 votes

You give to each number a letter:

Number 1: x

Number 2: y

The sum of two numbers is 2490:


x+y=2490

8.5% of x is equal to 6.5% of y:


x\cdot(8.5)/(100)=y\cdot(6.5)/(100)

You use the equations above to find the numbers by substitution method:

1. Solve one of the variables in the first equation:


x=2490-y

2. Substitute the variable x in the second equation by the value in step 1:


(2490-y)\cdot(8.5)/(100)=y\cdot(6.5)/(100)

3. Solve the equation in step 2 and find the value of y:


(2490-y)0.085=0.065y

Remove parenthesis multipliying 0.085 for both terms in the parenthesis:


211.65-0.085y=0.065y

Add 0.085y in both sides of the equation:


\begin{gathered} 211.65-0.085y+0.085y=0.065y+0.085y \\ 211.65=0.15y \end{gathered}

Divide into 0.15 both sides of the equation:


\begin{gathered} (211.65)/(0.15)=(0.15)/(0.15)y \\ \\ 1411=y \end{gathered}

4. Use the value of y to find x:


\begin{gathered} x=2490-y \\ x=2490-1411 \\ x=1079 \end{gathered}

Then, the numbers are x=1079 and y=1411

User John Hanley
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