Respuesta :

musiclover10045

AB:BC=3:4
90:(10x-20)=3:4
3(10x-20)=90×4
30x-60=360
30x=420

420/30=14


x=14
They are in ratio 4:3 so even the sides are in ratio.

Solve this with a proportion:

90:(10x-20) = 3:4

Multiply the means and extremes

3*(10x-20) and 4*90

30x-60 = 360

30x = 360+60

30x = 420

30x/30 = 420/30

x = 14

You can also solve it as an equation

since we said ab/bc = 3/4

[tex] \frac{90}{10x-20} = \frac{3}{4} [/tex]

Factorize 10x-20 as 10(x-2) and do LCM between denominators -> 20(x-2)

[tex] \frac{90}{10(x-2)} = \frac{3}{4} [/tex]

[tex] \frac{180}{20(x-2)} = \frac{15(x-2)}{20(x-2)} [/tex]

Multipli both fractions for 20(x-2) to delete denominator

Determine the range x-2 ≠ 0

x ≠ 2

180 = 15(x-2)

180 = 15x - 30

-15x = -30-180

-15x = -210

15x = 210

[tex] \frac{15}{15}x = \frac{210}{15} [/tex]

x = 14

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