The ratio of the number of ladies and gentlemen in a party is 3:4. If eight ladies join the party, the ratio of ladies and gentlemen would become 5:4. Find the number of gentlemen in the party.
Question
The ratio of the number of ladies and gentlemen in a party is 3:4. If eight ladies join the party, the ratio of ladies and gentlemen would become 5:4. Find the number of gentlemen in the party.
Solution
Let's solve this step by step:
Step 1: Let's assume the number of ladies and gentlemen in the party initially are 3x and 4x respectively.
Step 2: According to the problem, if eight ladies join the party, the ratio of ladies to gentlemen becomes 5:4. So, we can write this as (3x+8)/4x = 5/4.
Step 3: Cross multiply to solve for x. We get 4*(3x+8) = 5*4x.
Step 4: Simplify this to get 12x + 32 = 20x.
Step 5: Rearrange the equation to find the value of x. We get 20x - 12x = 32, which simplifies to 8x = 32.
Step 6: Solve for x. We get x = 32/8 = 4.
Step 7: Substitute x = 4 into 4x (the number of gentlemen) to find the number of gentlemen in the party. We get 4*4 = 16.
So, there are 16 gentlemen in the party.
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