Samuel and Jill had 576 stamps in all. Samuel gave 1/7 of his stamps to Jill. Then, Jill gave 1/4 of the total number of stamps she now had to
Samuel. In the end, both of them had the same number of stamps.
What was the difference in the number of stamps they each had at first?

128

Step-by-step explanation:

Sam has X stamps.

Jill has (576-X) Stamps.

X-x/7 = 6x/7 = Sam's bal.

576-x + x/7 = 576 - 6x/7 = Jill's bal.

1/4(576-6x/7) = 144 - 6x/28

3/4(576-6x/7) = 432 - 9x/14 = Jill's new

bal.

6x/7 + 144-6x/28 = 144 + 24x/28-6x/28 =

144 + 9x/14 = Sam's new bal.

Jill's new bal = Sam's new bal

432 - 9x/14 = 144 + 9x/14

18x/14 = 144-432 = 288

18x = 4032

X = 224

576-X = 576-224 = 352.

Difference = 352 - 224= 128

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9