Question

If the sum of 4 times a number a and 3 times a number b is equal to the sum of number b and seven times the number a, then what is the value of a:b?

Answer 1

Solution :

Sum of 4 times a number A and 3 times a number B i.e. 4A+3B is equal to sum of number B and seven times the number A i,e, B+7A.

$4A+3B=B+7A\\\\3B-B=7A-4A\\\\2B=3A\\\\\dfrac{2}{3}=\dfrac{A}{B}$

So, ratio of A to B is 2:3.

Answer 2

The value of a:b will be 2:3.

Given,

The sum of 4 times a number a and 3 times a number b equals the sum of number b and seven times the number a.

To Find,

The value of a:b.

Solution,

So, let's solve the question using the given information,

The Sum of 4 times a number A and 3 times a number B,

∵ 4A + 3B

The Sum of number B and seven times the number A are equal,

∵ B + 7A

Then,

⇒4A + 3B = B + 7A

⇒3B - B = 7A - 4A

⇒2B = 3A

$\frac{2}{3} = \frac{A}{B}$

A:B = 2:3.

The value of a:b will be 2:3.

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