Spice Kitchen Arithmetic

We can carefully set up an equation that relates the pounds of pepper to the total pounds of spice mix. We know that the amount of pepper should be half the total amount of spice mix, and we're solving for the amount of salt-and-pepper mix that we should add.

We start with 2 pounds of spice mix that contains 6/15 pounds of pepper. For every p pounds of salt-and-pepper mix we add, we add 0.65p pounds of pepper to the spice mix. So we can write our equation as follows: $\frac{6}{15} + 0.65p = \frac{1}{2}(2+p)$ $\frac{6}{15} + \frac{13}{20}p = 1+\frac{1}{2}p$ $\frac{3}{20}p = \frac{9}{15}$ $\boxed{p = 4}$

$Let:$ $x =$ mix which consists of 65% pepper and 35 % salt

$\frac{(\frac{6}{15} + 0.65x)}{(2 + x)} = 0.5$

$2(\frac{6}{15} + 0.65x) = (2+x)$

$\frac{12}{15} + 1.3x = 2 + x$

$1.3x - x = 2 - \frac{12}{15}$

$0,3x = 1.2$

$\boxed{x =\frac{1.2}{0.3} = 4}$

Total number of pounds in the sack is $2$ .

Now, the final condition we want is that half of the bag should be pepper.Thus, $\dfrac{\text{new weight of the bag}}{\text{new weight of pepper}} = \dfrac{2}{1}$ .

This just means that the amount of stuff in the bag is twice the amount of pepper.

Let the amount of pounds added to the bag be $x$ .

Now, $\dfrac{2 + x}{\left( \dfrac{6}{15} + 0.65x \right)} = \dfrac{2}{1}$

$\dfrac{18}{15} = 0.3x$

The $0.65x$ is because, for every $x$ pounds, $65 \%$ of it will be pepper.

Thus, solving the equation above to get $x$ , we find that $\boxed{ x = 4}$

Out of 2-pound sack we have 6/15 pounds of pepper=0.4 pounds

The rest of the mixture consists of 1.6 pounds of (cinnamon and cumin).

Given salt-and-pepper mix has 65% pepper and 35% salt.

Let the no: of pounds of salt-and-pepper mix be x

Then,the no: of pounds of pepper should be equal to the rest of mixture (As we need exactly half pepper)

0.4 + x 0.65 = 1.6 + x 0.35

Solving this we get x=4

Hence,4 pounds of salt-and-pepper mix must be added in order to have a mix that is exactly half pepper.

Let the no. of required pounds be x. Equation: (65x/100) + (6/15) = (50/100) X (2 + x) Solve it. You will get x= 4 pounds Hurray!

let pounds of the salt-and-pepper mix must he add = X

THEN 6/15 +0.65X = 0.5(2+X)

             X = 4

Let x be the pounds added. Then, 6/15 + 65x/100 = 1+x/2 9/15 = 15x/100 x = 900/225 or x = 4

Let the required amount of the salt-and-pepper mix be 'p' pounds.

Then, 6/15 + 0.65p = 1/2 x (2+p)

Solving we get, p = 4

Therefore, 4 pounds of the salt-and-pepper mix he must add, in order to have a mix that is exactly half pepper.

Start with 6/15 pounds pepper out of 2 pounds. Add x pounds of pepper-salt mix. pepper is now 6/15 + 0.65x while total is 2+x, so 0.4 + 0.65x = 0.5(2+x) so 0.4 + 0.65x = 1 + 0.5x so 0.15x = 0.6 so x = 0.6 / 0.15 = 4

Let P be the number of pounds of pepper we have, S = the total number of pounds of salt, cinnamon and cumin, T = the total amount we have of everything and X be the number of pounds of the salt and pepper mix we add, and so this is the value we are looking for.

T = 6/15 * P + 24/15 * S + (0.65P + 0.35S)X

T = 0.4P + 1.6S + 0.65PX + 0.35SX

Factorising that we get

T = (0.4 + 0.65X)P + (1.6 + 0.35X)S

We know the ratio of pepper to other spices is 1:1, therefore

0.4 + 0.65X = 1.6 + 0.35X

0.3X = 1.3

$\boxed{X = 4}$

Let the amount of salt and pepper mix to be added to the 2 pound sack be X pounds. Then the ratio of pepper to the final mixture is (6/15 + 0.65X)/(2+X) ans this must be equal to 1/2. Solving for X, we get X=4 pounds.