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Three whole numbers have a sum of 118

The ratio of the first number to the second number is 5:3

The ratio of the second number to the third number is 4:9

What are the three numbers?
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Sagot :

peraltakhaecee

17

18

10

that's the answer

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Answer:

40, 24, 54

Step-by-step explanation:

let the 3 numbers be x, y and z

then

[tex]\frac{x}{y}[/tex] = [tex]\frac{5}{3}[/tex] ( cross- multiply )

5y = 3x ( divide both sides by 5 )

y = [tex]\frac{3}{5}[/tex] x

and

[tex]\frac{y}{z}[/tex] = [tex]\frac{4}{9}[/tex] ( cross- multiply )

4z = 9y ( divide both sides by 4 )

z = [tex]\frac{9}{4}[/tex] y = [tex]\frac{9}{4}[/tex] × [tex]\frac{3}{5}[/tex] x = [tex]\frac{27}{20}[/tex] x

The 3 numbers are now expressed in terms of x , then adding gives

x + [tex]\frac{3}{5}[/tex] x + [tex]\frac{27}{20}[/tex] x = 118

multiply through by 20 to clear the fractions

20x + 12x + 27x = 2360

59x = 2360 ( divide both sides by 59 )

x = 40 ← first number

y = [tex]\frac{3}{5}[/tex] × 40 = 3 × 8 = 24 ← second number

z = [tex]\frac{27}{20}[/tex] × 40 = 27 × 2 = 54 ← third number

The 3 numbers are 40, 24, 54

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