How many different 5-digit numbers can you write using each of the digits 0, 1, 2, 3, 4 exactly once?
1 answer:
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Answer:
There are 120 people in the marching band.
Step-by-step explanation:
Let no. of people in the band be x.
In the first rectangular arrangement,
Width of rectangle () = w people.
Length of rectangle () = (w-7) people
Therefore,
no. of people in the band(x) = Area of the rectangle = Product of width and Length
x = width length
x = (equation 1);
In the second rectangular arrangement,
Width of rectangle () = (w-3) people.
Length of rectangle () = (w-5) people
Therefore,
no. of people in the band(x) = Area of the rectangle = Product of width and Length
x = width length
x = (equation 2);
Therefore, from equation 1 and equation 2 , we get,
Therefore,
w = 15 (equation 3)
From equation 1 and equation 3, we get
x =
x = 120.
Therefore,
no. of people in the marching band = 120 people
We can rephrase the question as "What percent of 50 is 20?".
"What percent ..." is an unknown. We'll use the variable x to represent this unknown.
The word 'of' in mathematics can mean 'multiply'. Likewise the word 'is' can mean 'equal'.
Now we have the phrase "20 equals to x times 50".
Or in an equation: 20 = x * 50
Solve for x.
20 = x * 50
= x <-- Divide both sides by 50
Simplify the fraction.
Convert the fraction into a decimal.
= 0.4
Convert the decimal into a percent.
0.4 = 40%
So, 40% is the answer.
"What percent ..." is an unknown. We'll use the variable x to represent this unknown.
The word 'of' in mathematics can mean 'multiply'. Likewise the word 'is' can mean 'equal'.
Now we have the phrase "20 equals to x times 50".
Or in an equation: 20 = x * 50
Solve for x.
20 = x * 50
Simplify the fraction.
Convert the fraction into a decimal.
Convert the decimal into a percent.
0.4 = 40%
So, 40% is the answer.