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QuestionFind NN so that x+N=3110x + N = \frac{31}{10} and xN=130\frac{x}{N} = \frac{1}{30} are equivalent. N= N =

Studdy Solution

STEP 1

Assumptions1. The two given equations are equivalent, which means they have the same solution for xx. . We are tasked to find the value of $$.

STEP 2

Let's start by expressing xx from the first equation in terms of $$.
x=3110−Nx = \frac{31}{10} - N

STEP 3

Now, let's substitute this expression for xx into the second equation.
x=130⇒3110−N=130\frac{x}{} = \frac{1}{30} \Rightarrow \frac{\frac{31}{10} - N}{} = \frac{1}{30}

STEP 4

Now, let's cross-multiply to get rid of the fractions.
30×(3110−N)=N30 \times (\frac{31}{10} - N) = N

STEP 5

implify the left side of the equation.
3×31−30=N3 \times31 -30 = N

STEP 6

Rearrange the equation to isolate $$.
3×31=30+N3 \times31 =30 + N

STEP 7

implify the right side of the equation.
3×31=313 \times31 =31

STEP 8

Finally, solve for $$ by dividing both sides of the equation by31.
=3×3131 = \frac{3 \times31}{31}

STEP 9

implify the right side of the equation to find the value of $$.
=3 =3So, the value of $$ that makes the two given equations equivalent is3.

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