The ratio of brenda’s age to jason’s age is 4: 5. in eight years the ratio will be 6: 7. how old is brenda now? a. 20 c. 28 b. 16 d. 12

Declarations

Let Brenda's age be B

Let Jason's age be J

Equations

Solution

Cross multiply both fractions

5B = 4J                             (1)

7(B + 8) = 6(J + 8)             Remove the brackets on both sides.

7B + 56 = 6J + 48             Subtract 48 from both sides

7B + 56 - 48 = 6J

7B + 8 = 6J                       (2)

Use Equation (1) to solve for J

5B = 4J   Divide by 4

5B/4 = J                                 Pult this result in equation 2

7B + 8 = 6*( 5B/4)

7B + 8 = 30*B/4

7B + 8 = 7.5 B                      Subtract 7B from both sides.

8 = 7.5B - 7B

8 = 0.5 B                              Divide by 0.5

B = 8/0.5

B = 16  <<<< Answer

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: