Soccer ratio for Math

Question

The ratio of players to soccer balls at practice sessions is 5:2.

How many soccer balls are needed for 20 players? Show all your work.

Answer 1

The question gives you a ratio of players to soccer balls, 5:2.

It is very important to label the ratio properly. If the ratio is 5:2 and we're told that the ratio is players to soccer balls, we know that the first number, 5, is the number of players and the second number, 2, is number of soccer balls.

Therefore, our known ratio is labeled as 5 players to 2 soccer balls, and the ratio in the question is 20 players to X soccer balls

You can write these two ratios as two fractions equivalent to each other, with number of players in the numerator and number of soccer balls in the denominator:

Given: Question:

Players: 5 = 20

Balls: 2 x

Now that it is set up, there are a couple ways to go about solving it.

1) When fractions are equal to each other, if you cross multiply, the products should be equal. Therefore 5 times x is equal to 20 times 2:

5x = 20 x 2

^ Simplified: 5x = 40

To solve for x, we must get x alone. We can do this by "undoing" the problem. Since x was multiplied by 5, we can get x alone by dividing it by 5; but to keep the equation balanced, we must divide both sides of the equation by 5. 5x divided by 5 is x, and 40 divided by 5 is 8.

5x = 40

5 5

x = 8

Players 5 = 20

Balls 2 8

The ratio is 20 : 8, meaning when there are 20 players, you need 8 soccer balls.

2) Another way to solve this it is to ask yourself what number can you multiply 5 by to get 20? (Answer: 4)

For fractions to remain equivalent, whatever you multiply the numerator by you must multiply the denominator by. So if you can say the numerator was multiplied by 4, the denominator must be multiplied by 4 as well. When we multiply the denominator (two) by 4, we get 8.

Given Question

Players: 5 (x4) 20

Balls: 2 (x4) ?

2 x 4 = 8

Answer: 8 soccer balls for 20 players

Answer 2

p : b :: 5 : 2

20 : b :: 5 : 2

5b = 40

b = 8

Answer 3

You have 2 soccer balls for every 5 players. How many soccer balls are needed for 20 players?

20/5=4

4*2=8

You will need 8 soccer balls for 20 players.

Answer 4

Hello Emilia,

A great way to figure out these ratio problems is to write out all the information and see how you can work from there.

I'd start out by writing that there's 2 balls for every 5 players and we want to know how many balls 20 players would need. We could create a proportion with fractions.

2 balls X balls

_________ = __________

5 players 20 players

Then we would cross multiply, so (5*X) = (2*20) --> our proportion is now 5X = 40.

Then to find X, we would divide both sides by 5 --> Our answer is that X = 8.

So our final answer is that 20 soccer players would need 8 balls.

I hope that this was helpful!

Answer 5

To make an equivalent ratio, you would need to multiply each by the same factor.

The given ration: 5 players: 2 soccer balls

If you multiply by ?? (5 x ?) : (2 x ?)

20 players: ? soccer balls

We know 5 x 4 is 20, so multiply each by 4

The given ration: 5 players: 2 soccer balls

If you multiply by 4 (5 x 4) : (2 x 4)

20 players: 8 soccer balls

OR

Make a visual

5 players: 2 Balls 5 players: 2 balls 5 players: 2 balls 5 players: 2 balls

Which would total: 20 players and 8 soccer balls

You would need 8 soccer balls for 20 players.

Answer 6

Eight (8) soccer balls are needed.

There are a variety of ways students might approach this problem based on their understanding of the required math. Younger students might draw a picture of five (5) players sharing two (2) soccer balls, and repeat this drawing three (3) more times to show twenty (20) students with eight (8) soccer balls.

Upper elementary students may want to use a ratio table, which would allow them to solve this specific problem, but also more easily recognize the ratio of 5:2 and solve for x players or y soccer balls.

A student might also solve using fractions as ratios like this:

y/20 - 2/5 = 0

Answer 7

Step 1: Set up variables

Let Soccer Balls = S

Step 2: Set up ratios

Our first ratio, equals 5:2

Our second ratio equals 20:S

Step 3: See the change in one ratio value, and do the same change to the other side

20 divided by 5 = 4.

From this, we see that the second ratio is equal to the first ratio, multiplied by 4 on both sides of the ratio.

So we have ...

5:2 = 20:S

And we know ...

2 x 4 = S

8 = S

Step 4: Show the answer

For 20 players, the amount of soccer balls we need is 8.