the ratio of boys to girls in a party is 3:5.if 6 more boys arrived and 4 girls left the party,the r...

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Tanong

the ratio of boys to girls in a party is 3:5.if 6 more boys arrived and 4 girls left the party,the ratio of boys to girls would be 5:6. how many are in the party originally?

Mga sagot sa #1 sa Tanong: the ratio of boys to girls in a party is 3:5.if 6 more boys arrived and 4 girls left the party,the ratio of boys to girls would be 5:6. how many are in the party originally?

Let x = number of boys originally

     y = number of girls originally

x/y = 3/5

   x = 3y/5

[(x + 6) / (y – 4)]  = 5/6

             6(x + 6) = 5 (y – 4)

             6x + 36 = 5y – 20

      6(3y/5) + 36 = 5y – 100

           18y + 180 = 25y – 20

          180 + 100  = 25y – 18y

                       7y = 280

                          y = 40

x = 3 (40)/5 = 120/5 = 24

Total number in the party originally = 40 + 24 = 64

64 are in the party originally

Mga sagot sa #2 sa Tanong: the ratio of boys to girls in a party is 3:5.if 6 more boys arrived and 4 girls left the party,the ratio of boys to girls would be 5:6. how many are in the party originally?

Original number of boys and girls:

Boys: 3x

Girls: 5x

New number of boys and girls:

Boys: 3x + 6

Girls: 5x – 4

Ratio: 5:6

Equation:

(3x+6) / (5x – 4) = 5/6

6(3x+6) = 5(5x-4)

18x + 36 = 25x – 20

25x – 18x = 36 + 20

7x/7 = 56/7

x = 8

Original number of boys and girls in the party:

Boys: 3(8) = 24 boys

Girls: 5(8) = 40 girls

There were originally a total of 64 boys and girls.

Check:

24:40 = 3:5

Divide each number by 8, the GCF:

(24/8) : (40/8) = 3:5

3:5 = 3:5  (True)

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