Question

The ratio of adults to children watching a school hockey game was
4 : 1. When 5 more adults and 20 more children came in, the ratio
changed to 7 adults for every 2 children. How many children in total
could there have been then?

a) 180
b) 170
c) 160
d) 150

Answer 1

Answer:

150 children

Step-by-step explanation:

Let the no. of adults and children be 4x and 1x respectively.

Then the ratios of adults to children watching game =4X: X

According to the question,when 5 more adults and 20 more children entered in the ratio, it was,

4X +5\ X+20=7/2

8X + 10= 7X + 140

X=130

Hence the total number of children could be

130+20=150 children

Answer 2

Answer:

The answer = 150 children

Step-by-step explanation:

Guess and Check method

Let's take 150 was the total number of children and put in a ratio

x:150

a:c

You don't what the new adult portion is

Do this : x:150 = 7/2

150 x 7/2 = 525  = 525:150 = 7/2

But this ratio of 525:150 is the new ratio. But what about the old ratio of 4:1

After that 5 more adults came and 20 more children came.

So what you would do after is to see if 525:150 is equal to the original ratio of adults to children = 4:1

525 - 5 = 520

150 - 20 = 130

520:130

The next step is to simplify this raito

520/13 = 40

130/13 = 10

40:10

But you could simplify it even further

40/10 = 4

10/10 = 1

4:1

There could have been 150 children at the school hockey game.