Question

Find a number whose half is equal to three times of some other number.​

Answer 1

Answer:

2

Step-by-step explanation:

Let n = the unknown number.

"Five (5) more than one-half the number n is 3 times the number n" can be translated mathematically into the following equation:

(1/2)n + 5 = 3n

n/2 + 5 = 3n

First, clear the equation of fractions by multiplying both sides by the only explicit denominator, 2, as follows:

2(n/2 + 5) = 2(3n)

2(n/2) + 2(5) = 2(3n)

(2/2)n + 10 = 6n

(1)n + 10 = 6n

n + 10 = 6n

Now, subtract n from both sides in order to begin isolating n on the right side as follows:

n - n + 10 = 6n - n

0 + 10 = 5n

10 = 5n

Now, divide both sides by 5 as follows in order to isolate n and thus solve the equation for n:

10/5 = (5n)/5

10/5 = (5/5)n

10/5 = (1)n

2 = n

CHECK:

(1/2)n + 5 = 3n

(1/2)(2) + 5 = 3(2)

2/2 + 5 = 6

1 + 5 = 6

6 = 6

Therefore, n = 2 is the desired number.

Answer 2

Answer:

Let n = the unknown number.

"Five (5) more than one-half the number n is 3 times the number n" can be translated mathematically into the following equation:

(1/2)n + 5 = 3n

n/2 + 5 = 3n

First, clear the equation of fractions by multiplying both sides by the only explicit denominator, 2, as follows:

2(n/2 + 5) = 2(3n)

2(n/2) + 2(5) = 2(3n)

(2/2)n + 10 = 6n

(1)n + 10 = 6n

n + 10 = 6n

Now, subtract n from both sides in order to begin isolating n on the right side as follows:

n - n + 10 = 6n - n

0 + 10 = 5n

10 = 5n

Now, divide both sides by 5 as follows in order to isolate n and thus solve the equation for n:

10/5 = (5n)/5

10/5 = (5/5)n

10/5 = (1)n

2 = n

CHECK:

(1/2)n + 5 = 3n

(1/2)(2) + 5 = 3(2)

2/2 + 5 = 6

1 + 5 = 6

6 = 6

Therefore, n = 2 is the desired number.

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