Answer:
Tom can either take 24 kicks and make 16 goals or 30 kicks and make 20 goals.
Step-by-step explanation:
Andre made 4 goals out of 6 kicks.
Tom wants to take more than 20 kicks and to make an equivalent fraction to Andre.
Possibility 1:
Let Tom makes 24 kicks.
To get 24, we need to multiply the denominator of Andre's fraction by 4.
So, [tex]\frac{4}{6} =\frac{16}{24}[/tex]
Therefore, Tom can take 24 kicks and make 16 goals.
Possibility 2:
Let Tom makes 30 kicks.
To get 30, we need to multiply the denominator of Andre's fraction by 5.
So, [tex]\frac{4}{6} =\frac{20}{30}[/tex]
Therefore, Tom can take 30 kicks and make 20 goals.
You can use the fact that to get the equivalent fractions, we can multiply the numerator and denominator of the given fraction with same integer.
Two of the infinite possible fractions of goals Tom can make are
[tex]\dfrac{16}{24} , \text{(16 goals in 24 kicks)}\\\\and\\\\\dfrac{20}{30}, \text{(20 goals in 30 kicks)}[/tex]
A fraction contains two parts. The above part is called numerator and the below part is called denominator.
Those fractions whose values are same even when they look different are called equivalent fractions.
You will find that equivalent fractions have a constant multiplied to both numerator and denominator of the fraction to which they are equivalent.
The given fraction for Andre's goals to kicks is 4 out of 6 or [tex]\dfrac{4}{6}[/tex]
Let the goal to kick counts' fraction for Tom be [tex]\dfrac{g}{k}[/tex]
where g = number of goals Tom do
k = number of kicks Tom takes.
Since goals and kicks are going to be in integer only, thus, we will multiply with integers only. And that will be equal to the fraction g/k
Let that integer be [tex]x[/tex]
Then,
[tex]g = 4 \times x\\k = 6 \times x[/tex]
Since Tom wants to take more than 20 kicks, thus,
[tex]k > 20\\6 \times x > 20\\x > 20/6 = 3.33..\\\\x = 4,5,6,... \: \: \: \text{(As x can be an integer only)}[/tex]
Thus, there can be infinite such equivalent fractions,
We need two, so let we take x = 4, and x = 5
Then
[tex]g = 4 \times x = 4 \times 4 = 16\\k = 6 \times x = 6 \tiems 4 = 24 > 20\\\\\dfrac{g}{k} = \dfrac{16}{20}[/tex]
[tex]g = 4 \times x = 4 \times 5 = 20\\k = 6 \times x = 6 \times 5 = 30 > 20\\\\\dfrac{g}{k} = \dfrac{20}{30}[/tex]
Thus,
Two of the infinite possible fractions of goals Tom can make are
[tex]\dfrac{16}{24} , \text{(16 goals in 24 kicks)}\\\\and\\\\\dfrac{20}{30}, \text{(20 goals in 30 kicks)}[/tex]
Learn more about equivalent fractions here:
https://brainly.com/question/8613911
