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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 .

Sagot :

You give to each number a letter:

Number 1: x

Number 2: y

The sum of two numbers is 2490:

[tex]x+y=2490[/tex]

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

[tex]x\cdot\frac{8.5}{100}=y\cdot\frac{6.5}{100}[/tex]

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

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

[tex]x=2490-y[/tex]

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

[tex](2490-y)\cdot\frac{8.5}{100}=y\cdot\frac{6.5}{100}[/tex]

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

[tex](2490-y)0.085=0.065y[/tex]

Remove parenthesis multipliying 0.085 for both terms in the parenthesis:

[tex]211.65-0.085y=0.065y[/tex]

Add 0.085y in both sides of the equation:

[tex]\begin{gathered} 211.65-0.085y+0.085y=0.065y+0.085y \\ 211.65=0.15y \end{gathered}[/tex]

Divide into 0.15 both sides of the equation:

[tex]\begin{gathered} \frac{211.65}{0.15}=\frac{0.15}{0.15}y \\ \\ 1411=y \end{gathered}[/tex]

4. Use the value of y to find x:

[tex]\begin{gathered} x=2490-y \\ x=2490-1411 \\ x=1079 \end{gathered}[/tex]

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

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