MHB Solve for J and B: Junhao & Bala Stamps Problem

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Junhao and Bala collect stamps, with the relationship between their collections defined by two equations. Junhao has 76 more stamps than Bala, leading to the equation J = 76 + B. Additionally, 1/3 of Junhao's stamps equals 3/5 of Bala's, resulting in J = (9/5)B. By substituting the first equation into the second, both J and B can be solved. This method clarifies the approach to finding the number of stamps each collector has.
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Junhao and Bala both collect stamps. 1/3 of Junhao's stamps is equal to 3/5 of Bala's stamps. Junhao has 76 more stamps than Bala. How many stamps does each of them have?

My answer:

Number of stamps Junhao have =J
Number of stamps Bala have = B

We know that Junhao has 76 more stamps than Bala => Junhao = 76 + Bala.

I'm not sure if this is a correct way to do it, but we know 1/3 of Junao's stamp equal to 3/5 of Bala's stamps.
so => (1/3)J = (3/5)BI got stuck and couldn't figure out a clear way to do this.
 
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Johnx said:
Number of stamps Junhao have =J
Number of stamps Bala have = B

We know that Junhao has 76 more stamps than Bala => Junhao = 76 + Bala.

Why don't you change the equation to following using J and B

$$J = 76 + B$$

and you already have the following equation,

$$ \frac{J}{3} = \frac{3B}{5} \implies J = \frac{9B}{5}$$

now you have two unknown variables and two equations. So you can find the values for J and B by substituting the J on the first equation from the second
 
BAdhi said:
$$ \frac{J}{3} = \frac{3B}{5} \implies J = \frac{9B}{5}$$
Thank you for this. I didn't see it this way.
 
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