The three numbers are in the ratio 4:5:6. If the sum of the largest and

the smallest number is equal to the sum of the second largest number

and 55. Find the numbers.

# The three numbers are in the ratio 4:5:6. If the sum of the largest and

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Answer:## Given :-

## To Find :-

## Solution :-

Let,[tex]\mapsto[/tex]

Firstnumber=4x[tex]\mapsto[/tex]

Secondnumber=5x[tex]\mapsto[/tex]

Thirdnumber=6xAccordingtothequestion,[tex]\implies \sf 6x + 4x =\: 5x + 55[/tex]

[tex]\implies \sf 10x =\: 5x + 55[/tex]

[tex]\implies \sf 10x – 5x =\: 55[/tex]

[tex]\implies \sf 5x =\: 55[/tex]

[tex]\implies \sf x =\: \dfrac{\cancel{55}}{\cancel{5}}[/tex]

[tex]\implies \sf x =\: \dfrac{11}{1}[/tex]

[tex]\implies \sf\bold{\green{x =\: 11}}[/tex]

Hence,therequirednumbersare:[tex]\dashrightarrow[/tex]

Firstnumber:[tex]\leadsto \sf 4x[/tex]

[tex]\leadsto \sf 4(11)[/tex]

[tex]\leadsto \sf 4 \times 11[/tex]

[tex]\leadsto \sf\bold{\red{44}}[/tex]

[tex]\dashrightarrow[/tex]

Secondnumber:[tex]\leadsto \sf 5x[/tex]

[tex]\leadsto \sf 5(11)[/tex]

[tex]\leadsto\sf 5 \times 11[/tex]

[tex]\leadsto \sf\bold{\red{55}}[/tex]

[tex]\dashrightarrow[/tex]

Thirdnumber:[tex]\leadsto \sf 6x[/tex]

[tex]\leadsto \sf 6(11)[/tex]

[tex]\leadsto \sf 6 \times 11[/tex]

[tex]\leadsto \sf\bold{\red{66}}[/tex]

[tex]\therefore[/tex]

Thenumbersare44,55and66respectively.[tex]\rule{150}{2}[/tex]

:-VERIFICATION[tex]\Rightarrow \sf 6x + 4x =\: 5x + 55[/tex]

Byputtingx=11weget,[tex]\Rightarrow \sf 6(11) + 4(11) =\: 5(11) + 55[/tex]

[tex]\Rightarrow \sf 66 + 44 =\: 55 + 55[/tex]

[tex]\Rightarrow \sf\bold{\purple{110 =\: 110}}[/tex]

Hence,Verified.[tex]\rule{150}{2}[/tex]

#Learnmore:3 Sum of three numbers which are in the ratio 3:4:5 is 60. What is the sum of their squares?

(A)1970

(B)1430

(C)1250

(D)1760

https://brainly.in/question/40125762

Provided:The three numbers are in the ratio4:5:6. & sum of the largest and smallest number is equal to the sum of2nd55.Need to find:Thethreerespectivenumbers.⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀❍ Let’s say, that the three numbers which are in the ratio be

4x,5xand6x.⠀⠀⠀⠀

[tex]\underline{\bigstar\:\pmb{ \frak{According \: to \: the \: given \: Question :}}}[/tex]

sumof the largest and smallest number is equal to thesumof2nd largest no. and55.⠀

[tex]:\implies\sf Largest \: no. + Smallest \: no. = 2nd \: largest \: no. + 55 \\\\\\:\implies\sf 6x + 4x = 5x + 55 \\\\\\:\implies\sf 10x = 5x + 55 \\\\\\:\implies\sf 10x – 5x = 55\\\\\\:\implies\sf 5x = 55\\\\\\:\implies\sf x = \cancel\dfrac{55}{5}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 11}}}}}\;\bigstar[/tex]

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀Therefore,

⠀⠀⠀⠀

445566⠀⠀⠀⠀

[tex]\therefore{\underline{\textsf{Hence, the three numbers are \textbf{44, 55 \sf{and} \textbf{66} \sf{respectively}.}}}}[/tex]⠀⠀⠀⠀