Question

if 2a+3b:3a-2b=19:9,finda:b?

Answer 1

Heya user,

( 2a + 3b ) / ( 3a - 2b ) = 19 / 9
=> 9 ( 2a + 3b ) = 19 ( 3a - 2b )
=> 18a + 27b = 57a - 38b
=> 38b + 27b = 57a - 18a
=> 65b = 39a
=> 39a / 65b = 1
=> a/b = 65/39
=> a/b = 5*13 / 3*13
=> a/b = 5/3

Therefore, a : b = 5 : 3

Answer 2

Concept

The ratio is a measure of how much of one quantity is present in the other. The common form for expressing the ratio of two quantities, "a" and "b", is a: b, which is read as "a is to b". The fractional format for this ratio is a / b. For further simplification, follow the same steps for ratios that you use to simplify fractions. a:b = a/b.

Given

We have given a ratio $2a+3b:3a-2b=19:9$ .

Find

We are asked to determine the ratio of $a:b$ .

Solution

It is given that  $\frac{2a+3b}{3a-2b} =\frac{19}{9}$

On cross multiplication, we get

$9(2a+3b)=19(3a-2b)\\18a+27b=57a-38b\\65b=39a\\\frac{65}{39}=\frac{a}{b}$

Therefore , a:b is equals to 65:39

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