Solve the following problems

Question

Solve the following problems.

1. Joshua multiplied his favorite number by itself three times. He added it to 6² and the sum is 10². What is his favorite number?

2. The product of the ages of some teenagers is expressed as 2² x 3⁴ x 5² x 7. Find out what their ages are.

3. By what number should 5³ be multiplied so that the product becomes equal to 25³?

4. By what number should 8⁴ be divided so that the quotient becomes equal to 64?

Answer 1

Hello, Ghe.

For problem 1:

Let x be Joshua's favorite number. If he multiplied it by itself 3 times, then he had x³ . He then added it to 6² and got 10² .So, x³ + 36 = 100

First, subtract 36 from both sides:

x³ + 36 - 36 = 100 - 36 = 64

x³ + 0 = 64

x³ = 64

x = 4

For problem 2:

Since we don't know how many teenagers there are, we will have to do some analyzing. The product of

their ages is (2x2)x(3x3x3x3)x(5x5)x7....

First, the 7 can only be multiplied by a 2 to get a product in the teens...7x2 = 14. That must be one teen's age. Next, 5 must be multiplied by a 3 to get a product in the teens...5x3 = 15. Since there are two 5's, there must be 2 fifteen year-olds. Now we have left:

2x3x3 = 18.

Therefore, there must be:

1- 14 year-old

2 - 15 year-olds

1 - 18 year-old

Problem 3:

5³ (x) = 25³ Since 25³ = (5²)³ = 5⁶

5³ (x) = 5⁶

Divide by sides by 5³ :

x = 5³ = 125

Problem 4:

8⁴ ÷ n = 64 = 8²

8⁴ ÷ 8² = 8²

n = 8² = 64

I hope this helps.