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Vikentia [17]
3 years ago
13

Solve the proportion for x

Mathematics
1 answer:
frez [133]3 years ago
7 0

\begin{gathered}\\ \sf\longmapsto \frac{49}{56}=\frac{x}{8}\end{gathered}

\begin{gathered}\\ \sf\longmapsto \cancel{\dfrac{49}{56}}=\frac{x}{8}\end{gathered}

\begin{gathered}\\ \sf\longmapsto \frac{7}{8}=\frac{x}{8}\end{gathered}

✎When the denominators are the same, set the numerators equal

\begin{gathered}\\ \sf\longmapsto 7=x\end{gathered}

  • ✎Swap the sides of the equation

\begin{gathered}\\ \sf\longmapsto x=7\end{gathered}

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When you reverse the digits in a certain two-digit number you decrease its value by 18. what is the number if the sum of its dig
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Lets start by defining the 2-digit number.

--------------------------------------------------------------
Define the number
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Let x be the digit in the tens place and y be the digit in the ones place.
The number is 10x + y
The reverse of the number is 10y + x 

Now we will construct the equations needed

--------------------------------------------------------------
Construct equations
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When the digits are reversed, the value decreases by 18:
(10x + y) - (10y + x) = 18 .    ← Apply distributive property
10x + y - 10y - x = 18            ←Combine like terms
9x - 9y = 18                           ←Divide by 9 through
x - y = 2

The sum of the digits is 12:
x + y = 12

Now that we have the two equations, we can solve for x and y.

--------------------------------------------------------------
Solve for x and y
--------------------------------------------------------------
x - y  = 2          ---------------------- (equation 1)
x + y = 12        ---------------------- (equation 2)

--------------------------------------------------------------
Make x the subject in equation 1
--------------------------------------------------------------
x - y = 2      ← Add y from both sides
    + y   +y       

x = 2 + y 

--------------------------------------------------------------
Substitute x = 2 + y into equation 2
--------------------------------------------------------------
x + y = 12                      ← Substitute x = 2 + y
2 + y + y = 12                ← combine like terms  
2 + 2y = 12                    ← Subtract 2 from both sides
-2           -2
2y = 10                          ← Divide by 2 on both sides
÷2    ÷2
y = 5

--------------------------------------------------------------
Substitute y = 5 into equation 1
--------------------------------------------------------------
x - y = 2                          ← substitute  y = 5
x - 5 = 2                          ← add 5 on both sides
   +5   +5
x = 7

Now we know the value of x and y. Lets find the 2-digit number.

--------------------------------------------------------------
Find the 2-digit number
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The number = 10x + y = 10(7) + 5 = 75

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Answer: The number is 75
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