Answer:
x=1
Step-by-step explanation:
Here,
[tex]15 \frac{x}{4} +18\frac{2}{3} =33\frac{11}{12}[/tex]
Simplifying,
[tex]15 \frac{x}{4} +18\frac{2}{3} =33\frac{11}{12} \\\\\frac{15*4+x}{4} +\frac{56}{3} =\frac{407}{12} \\\\\frac{3(60+x)+4*56}{12} =\frac{407}{12} \\\\\frac{180+3x+224}{12} =\frac{407}{12} \\\\\frac{404+3x}{12} =\frac{407}{12} \\\\12*407=12(404+3x)\\\\4884=4848+36x\\\\36x=4884-4848\\\\36x=36\\\\x=36/36\\\\x=1[/tex]
Step-by-step explanation:
Given: {15(x/4)} + {18(2/3)} = {33(11/12)}
We have to find the value of missing numerator (x)
Solution:
Given equation is {15(x/4)} + {18(2/3)} = {33(11/12)}
Convert the mixed fractions to inproper fractions, on both LHS and RHS.
= {(15*4 + x)/4} + {(18*3 + 2)/3} = {(33*12 + 11)/12}
Multiply the numerator numbers on both LHS and RHS.
= {(60+x)/4} + {(54+2)/3} = {(396+11)/12}
Add the numerator variables and Constants on both LHS and RHS.
= {(60x)/4} + (56/3) = 407/12
Write all the numerators with common denominator by converting them into like fractions on LHS.
Take the LCM of the denominator on LHS
,i.e., 3 and 4 is 12.
= {(60x*3 + 56*4)/12} = 407/12
= {(180x + 224)/12} = 407/12
Since, (a/b) = (c/d) ⇛ a(d) = b(c)⇛ad = bc
Where, a = 180x + 224, b = 12, c = 407 and d = 12
On applying cross multiplication then
⇛12(180x + 224) = 12(407)
Multiply the number outside of the brackets with numbers on brackets on both LHS and RHS.
⇛2160x + 2688 = 4884
Shift the number 2688 from LHS to RHS, changing it's sign.
⇛2160x = 4884 - 2688
Subtract the values on RHS.
⇛2160x = 2196
Shift the constant 2160 from LHS to RHS, changing it's sign.
⇛ x = 2196/2160
Simplify or reduce the RHS fraction in simplest form by using cancelling method to get the final value of (x).
= {(2196÷3)/(2160÷3)}
= (732/720)
= {(732÷3)/(720÷3)}
= (244/240)
= {(244÷2)/(240÷2)}
= (122/120)
= {(122÷2)/(120÷2)}
= (61/60)
Answer: Hence, the value of x for the given problem is 61/60.
EXPLORE MORE:
Verification:
Check whether the value of x for the given problem is true or false.
If x = 61/60 then LHS of the equation is
{15(x/4)} + {18(2/3)} = {33(11/12)}
⇛[{60(61/60)}/4] + {18(2/3)} = {33(11/12)}
⇛[{(60* 61)/60}/4] + {(18*3 + 2)/3} = {(33*12 + 11)/12}
⇛[{(3660/60)}/4] + {(54+2)/3} = {(396+11)/12}
⇛(12/4) + (56/3) = (407/12)
⇛{(12*3 + 56*4)/12} = 407/12
⇛{(183 + 224)/12} = 407/12
⇛(407/12) = 407/12
⇛407/12 = 407/12
On comparing with both sides, we notice that LHS = RHS is true for x = 61/60.
Hence, verified.
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