Solve the following

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 2²x3⁴x5²x7. 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.

First of all, you seem to have all of your questions answered except #2, which definitely can be answered with the given information.

Problem 2:

Since we don't know how many teenagers there are, we will have to do some thinking. 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

Answer 2

Problem 1

6²+x³=10²

36+x³=100

x³=64

x=4 <-- Favorite number is 4

Problem 2

Not enough information

Problem 3

5³x=25³

5³x=(5²)³

5³x=5⁶

x=5³=125

Problem 4

8⁴/x = 64

8⁴/x = 8²

8⁴/8² = x

8² = x

x = 64

Answer 3

1. not enough information
2. not enough information
3. Answer: 125

cube five that equals 125.... cube 25 that equals 15,625 ..... 15,625 divided by 125 equals 125...therefore 125 is the answer

4.Answer: 64

8 to the 4th power is 4,096 ....divide 4,096 by 64 and the answer is 64