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On friday, the ratio of the number of adults to boys to girls visiting a zoo was 7:6:5. on saturday, the number of adults visiting the zoo remained the same. however, the number of boys increased by 50% and the number of girls decreased by 40%.

a)what was the ratio of the number of adults to boys to girls visiting the zoo on saturday?
b)on friday, 627 boys and girls visited the zoo. what was the total number of visitors at the zoo on saturday?



Answer :

Part a

The ratio of the number of adults to boys to girls visiting the zoo on Saturday was 7:9:3

Part b

The total number of visitors at the zoo on Saturday was 1083

Given,

The ratio of the number of adults to boys to girls visiting a zoo= 7:6:5

Consider the number of adults, boys and girls visiting the zoo was 7x, 6x and 5x respectively

Number of boys increased =50%

Number of girls decreased =40%

Increase in boys =[tex]6x+6x(\frac{50}{100})[/tex]

[tex]=6x(1+\frac{50}{100}) \\=6x(1+0.5)\\=6x(1.5)\\=9x[/tex]

Decrease in girls=[tex]5x-5x(\frac{40}{100})[/tex]

[tex]=5x(1-\frac{40}{100})[/tex]

=5x(1-0.4)

=5x(0.6)

=3x

The ratio of the number of adults to boys to girls visiting the zoo on Saturday = 7:9:3

Part b

Number of boys and girls visited on Friday =627

The ratio of the number of adults to boys to girls visiting a zoo= 7:6:5

Therefore,

6x+5x=627

11x=627

x=[tex]\frac{627}{11}[/tex]

x=57

The ratio of the number of adults to boys to girls visiting the zoo on Saturday = 7:9:3

Then,

7x+9x+3x=19x

Substitute the value of x in the equation

19×57=1083

Hence, the total number of visitors at the zoo on Saturday=1083

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