1. ## Simultaneous Equation Problem...

Jane wants to prepare a special diet for her pets. She requires a food mixture that contains, among other things, 29 ounces of protein and 6 ounces of fat. Food mixes are available with the compositions shown in the table. How many ounces of each mix should she use to prepare the diet mix?

In Mix A, there are 20% of protein and 2% of fat.
In Mix B, there are 10% of protein and 6% of fat.

I have no idea how to solve it but I know the answer is 114 ounces of Mix A and 62 ounces of Mix B. Thx.

2. You have

$\displaystyle \frac{2}{10}x_A + \frac{1}{10}x_B = 29$
$\displaystyle \frac{2}{100}x_A + \frac{6}{100}x_B = 6$

Solve the first equation for $\displaystyle x_A$ and you get
$\displaystyle 145 - \frac{1}{2}x_B$
Replace $\displaystyle x_A$ in the second equation with that solution and solve for $\displaystyle x_B$, which should give you $\displaystyle x_B = 62$.

3. Originally Posted by clarebear14
Jane wants to prepare a special diet for her pets. She requires a food mixture that contains, among other things, 29 ounces of protein and 6 ounces of fat. Food mixes are available with the compositions shown in the table. How many ounces of each mix should she use to prepare the diet mix?

In Mix A, there are 20% of protein and 2% of fat.
In Mix B, there are 10% of protein and 6% of fat.

I have no idea how to solve it but I know the answer is 114 ounces of Mix A and 62 ounces of Mix B. Thx.
let x = oz of mix A
y = oz of mix B

.2x + .1y = 29

.02x + .06y = 6

------------------
multiply the first equation by 10, the second by 100

2x + y = 290

2x + 6y = 600

use elimination ...

5y = 310

y = 62

and the value for x will follow.

4. Originally Posted by clarebear14
Jane wants to prepare a special diet for her pets. She requires a food mixture that contains, among other things, 29 ounces of protein and 6 ounces of fat. Food mixes are available with the compositions shown in the table. How many ounces of each mix should she use to prepare the diet mix?

In Mix A, there are 20% of protein and 2% of fat.
In Mix B, there are 10% of protein and 6% of fat.

I have no idea how to solve it but I know the answer is 114 ounces of Mix A and 62 ounces of Mix B. Thx.
Let the number of ounces of Mix A be x.

Let the number of ounces of Mix B be y.

$\displaystyle \frac{20}{100}x+\frac{10}{100}y=29$

$\displaystyle \frac{2}{100}x+\frac{6}{100}y=6$

Solving these 2 equations, we get x=114 and y=62.